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Study of the fluctuation of spectra of random operators

Research Project

Project/Area Number 17540100
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKeio University (2007)
University of Tsukuba (2005-2006)

Principal Investigator

MINAMI Nariyuki  Keio University, School of Medicine, Professor (10183964)

Co-Investigator(Kenkyū-buntansha) NAKAMO Fumihiko  Keio University, Faculty of Science, Associate Professor (10291246)
NOMASA Ueki  Kyoto University, Graduate School of Human and Environmental Studiess, Associate Professor (80211069)
MAKINO Hironori  Tokai University, School of Information Ttchnology and Electrnics, Associate professor (40338786)
NAGAO Taro  Nagoya University, Graduate School of Mathematics, Associate Professor (10263196)
鈴木 由紀  慶應義塾大学, 医学部, 講師 (30286645)
磯崎 洋  筑波大学, 大学院数理物質科学研究科, 教授 (90111913)
笠原 勇二  筑波大学, 大学院数理物質科学研究科, 教授 (60108975)
三河 寛  筑波大学, 大学院・数理物質科学研究科, 講師 (10219602)
籠屋 恵嗣  筑波大学, 大学院数理物質科学研究科, 助手 (40323258)
Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2005: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordslevel statistics / random operators / quantum chaos / Anderson model / branching process / Galton-Watson tree / 数理物理 / 確率論 / unfolding / Galton-Watson樹形図 / 局所極限定理
Research Abstract

In this project, we made a general approach to the statistical fluctuation of spectra of random operators from the viewpoint of point process theory, and at the same time, studied the level statistics for a concrete random Schrodinger operator In addition to these researches, we made a probabilistic investigation of random trees, a study motivated by questions of estimating traces of random matrices. Main results are the followings:
1. A mathematical formulation was made of the notion of "unfolding' which is a procedure of normalizing the spectrum of a random operator, so that it can be viewed as a typical realization of a stationary point process.
2. An attempt was made to prove that the unfolded spectrum of the discrete random Schrodinger operator looks like a typical realization of the Poisson point process, and it was clarified that the proof boils down to estimating the probability that two disjoint intervals simultaneously contain eigenvalues of the operator. However, because of the difficulty in obtaining this estimate, the whole proof is still incomplete.
3. Concerning a class of random trees obtained as trajectories of discrete time branching processes, a local limit theorem was obtained for the number of vertices having k children for k=0, 1, 2, .
4. A general extension theorem was obtained for the construction of a probability measure on the space of trees whose vertices have "marks" representing for example spatial location, age, types etc. of vertices.

Report

(4 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report

Research Products

(100 results)

All 2008 2007 2006 2005 Other

All Journal Article (50 results) (of which Peer Reviewed: 19 results) Presentation (50 results)

  • [Journal Article] Theory of Point Processes and Some Basic Notions in Energy Level Statistics2007

    • Author(s)
      Nariyuki Minami
    • Journal Title

      CRM Proceedings and Lecture Notes 42

      Pages: 353-398

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Eigenfunction statistics in the Anderson model2007

    • Author(s)
      Rowan Killip and Fumihiko Nakano
    • Journal Title

      Annales Henri Poincare 8

      Pages: 27-36

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Distribution of Localization Centers in Some Discrete Random Systems2007

    • Author(s)
      Fumihiko Nakano
    • Journal Title

      Reviews in Mathematical Physics 19

      Pages: 941-965

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Pfaffian expression for random matrix correlation functions2007

    • Author(s)
      Taro Nagao
    • Journal Title

      Journal of Statistical Physics 129

      Pages: 1137-1158

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Spectral density of sparse sample covariance matrices2007

    • Author(s)
      Taro Nagao and Toshiyuki Tanaka
    • Journal Title

      Journal of Physics A 40

      Pages: 4973-4987

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Semiclassical approach to parametric spectral correlation with spin 1/22007

    • Author(s)
      Taro Nagao and Keiji Saito
    • Journal Title

      Journal of Physics A 40

      Pages: 12055-12070

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Inverse boundary problem in the horospheres-a link between Hyperbolic geometry and electrical impedance tomography2007

    • Author(s)
      Hiroshi Isozaki
    • Journal Title

      Inverse Problem and Imaging 1

      Pages: 107-134

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Theory of Point Processes and Some Basic Notions in Energy Level Statistics2007

    • Author(s)
      Minami, Nariyuki
    • Journal Title

      CRM Proceedings and Lecture Notes 42

      Pages: 353-398

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Distribution of Localization Centers in Some Discrete Random Systems2007

    • Author(s)
      Nakano, Fumihiko
    • Journal Title

      Reviews in Mathematical Physics 19

      Pages: 941-965

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Journal Article] Eigenfunction statistics in the Anderson model2007

    • Author(s)
      Rowan, Killip, Fumihiko, Nakano
    • Journal Title

      Annales Henri Poincare 8

      Pages: 27-36

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Distribution of localization centers in some random systems2007

    • Author(s)
      Fumihiko, Nakano
    • Journal Title

      Reviews in Mathematical Physics 19

      Pages: 941-965

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Pfaffian expressions for random matrix correlation functions2007

    • Author(s)
      Taro, Nagao
    • Journal Title

      Journal of Statistical Physics 129

      Pages: 1137-1158

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Spectral density of sparse sample covariance matrices2007

    • Author(s)
      Taro, Nagao, Toshiyuki, Tanaka
    • Journal Title

      Journal of Physics A 40

      Pages: 4973-4987

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Semiclassical approach to parametric spectral correlation with spin 1/22007

    • Author(s)
      Taro, Nagao, Keiji, Saito
    • Journal Title

      Journal of Physics A 40

      Pages: 12055-12070

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Inverse, boundary problem in the horospheres - a link between hyperbolic geometry and electrical impedence tomography2007

    • Author(s)
      Hiroshi, Isozaki
    • Journal Title

      Inverse Problem and Imaging 1

      Pages: 107-134

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Theory of Point Processes and Some Basic Notions in Energy LevelStatistics2007

    • Author(s)
      Minami, Nariyuki
    • Journal Title

      CRM Proceedings and Lecture Notes 42

      Pages: 353-398

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pfaffian Expressions for Random Matrix Correlation Functions2007

    • Author(s)
      Nagao, Taro
    • Journal Title

      Journal of Statistical Physics 129

      Pages: 1137-1158

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eigenfunction statistics in the localized Anderson model2007

    • Author(s)
      Killip, R., Nakano, F.
    • Journal Title

      Annales Henri Poincare 8・1

      Pages: 27-36

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Inverse boundary problem in the horosperes-a link between hyperbolic geometry and electrical impedence tomography2007

    • Author(s)
      Isozaki, H.
    • Journal Title

      Inverse Probl. Imaging 1・1

      Pages: 107-134

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The repulsion between localization centers in the Anderson model2006

    • Author(s)
      Fumihiko Nakano
    • Journal Title

      Journal of Statistical Physics 123

      Pages: 803-810

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] The spectrum of the Schrodinger operators with Poisson type random Potential2006

    • Author(s)
      Kazunori Ando, Akira Iwatsuka, Msahiro Kaminaga and Fumihiko Nakano
    • Journal Title

      Annale Henri Poincare 7

      Pages: 145-160

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Correlation functions for random involutions2006

    • Author(s)
      Peter Forrester, Taro Nagao and Eric Rains
    • Journal Title

      International Mathematics Research Notices 2006

      Pages: 1-35

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Brownian representation of a class of Levy processes and its Application to occupation times of diffusion processes2006

    • Author(s)
      Yuji Kasahara and Shinzo Watanabe
    • Journal Title

      Illinois Journal of Mathematics 50

      Pages: 515-539

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] The spectrum of the Schrodinger operators with Poisson type random Potential2006

    • Author(s)
      Kazunori, Ando, Akira, Iwatsuka, Msahiro, Kaminaga, Fumihiko, Nakano
    • Journal Title

      Annales Henri Poincare 7

      Pages: 145-160

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Correlation functions for random involutions2006

    • Author(s)
      Peter, Forrester, Taro, Nagao, Eric, Rains
    • Journal Title

      International Mathematics Research Notices 2006

      Pages: 1-35

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Brownian representation of a class of Levy processes and its application to occupation times of diffusion processes2006

    • Author(s)
      Yuji, Kasahara, Shinzo, Watanabe
    • Journal Title

      Illinois Journal of Mathematics 50

      Pages: 515-539

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] The repulsion between localization centers in the Anderson model2006

    • Author(s)
      Nakano, F.
    • Journal Title

      J. Stat. Phys. 123・4

      Pages: 803-810

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The spectrum of the Schroedinger operators with Poisson type random potential2006

    • Author(s)
      Ando, K., Iwatsuka, A., Kaminaga, M., Nakano, F.
    • Journal Title

      Annales Henri Poincare 7・1

      Pages: 145-160

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Correlation functions for random involutions2006

    • Author(s)
      Forrester, P., Nagao, T., Rains, E.
    • Journal Title

      Int. Math. Res. Not. 2006・89796

      Pages: 1-35

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Brownian representation of a class of Levy processes and its application to occupation times of diffusion processes2006

    • Author(s)
      Kasahara, Y., Watanabe, S.
    • Journal Title

      Illinois J. Math. 50・1-4

      Pages: 515-539

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On the number of vertices with a given degree in a Galton-Watson tree2005

    • Author(s)
      Nariyuki Minami
    • Journal Title

      Advances in Applied Probability 37

      Pages: 229-264

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Long-range spectral statistics of classically integrable systems2005

    • Author(s)
      Hironori Makino and Shuichi Tasaki
    • Journal Title

      Progress of Theoretical Physics 114

      Pages: 929-941

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Occupation time theorem for a class of one-dimensional diffusion Processes2005

    • Author(s)
      Yuji Kasahara and Shinzo Watanabe
    • Journal Title

      Periodica Mathematica Hungarica 50

      Pages: 175-188

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Sequential interval estimation of a location parameter with the fixed width in the uniform distribution with an unknown scale parameter2005

    • Author(s)
      Masafumi Akahira and Kenichi Koike
    • Journal Title

      Sequential Analysis 24

      Pages: 63-75

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Primes in arithmetic progression to spaced moduli2005

    • Author(s)
      Hiroshi Mikawa and Temenoujka Peneva
    • Journal Title

      Archiv der Mathematck(Basel) 84

      Pages: 239-248

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Free boundary problem from two component system on Z2005

    • Author(s)
      Keishi Komoriya
    • Journal Title

      Journal of Mathematical Sciences, the University of Tokyo 12

      Pages: 239-248

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On the Number of Vertices with a Given Degree in a Galton-Watson tree2005

    • Author(s)
      Minami, Nariyuki
    • Journal Title

      Advances in Applied Probability 37

      Pages: 229-264

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] spectral statistics of classically integrable systems2005

    • Author(s)
      Hironori, Makino, Shuichi, Tasaki, Long-range
    • Journal Title

      Progress in Theoretical Physics 114

      Pages: 929-941

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Occupation time theorem for a class of one-dimensional diffusion Processes2005

    • Author(s)
      Yuii, Kasahara, Shinzo, Watanabe
    • Journal Title

      Periodica Mathematica Hungarica 50

      Pages: 175-188

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Sequential interval estimation of a location parameter with the fixed width in the uniform distribution with an unknown scale parameter2005

    • Author(s)
      Masafumi, Akahira, Kenichi, Koike
    • Journal Title

      Sequential Analysis 24

      Pages: 63-75

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Primes in arithmetic progression to spaced moduli2005

    • Author(s)
      Hiroshi, Mikawa, Temenoujka, Peneva
    • Journal Title

      Archiv der Mathematik (Basel) 84

      Pages: 239-248

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Free boundary problem from two component system on z2005

    • Author(s)
      Keishi, Komoriya
    • Journal Title

      Journal of Mathematical Sciences, the University of Tokyo 12

      Pages: 239-248

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On the number of vertices with a given degree in a Galton-Watson tree2005

    • Author(s)
      MINAMI, N.
    • Journal Title

      Adv.in Appl.Probab. 37・1

      Pages: 229-264

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Sequential interval estimation of a location parameter with the fixed width in the uniform distribution with an unknown scale parameter2005

    • Author(s)
      Akahira, M., Koike, K.
    • Journal Title

      Sequential Anal. 24・1

      Pages: 63-75

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Primes in arithmetic progression to spaced moduli2005

    • Author(s)
      Mikawa, H., Peneva, T.P.
    • Journal Title

      Arch.Math.(Basel) 84・3

      Pages: 239-248

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Free boundary problem from two component system on Z2005

    • Author(s)
      Komoriya, K.
    • Journal Title

      J.Math.Sci.Univ.Tokyo 12・2

      Pages: 141-163

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Long-range spectral statistics of classically integrable systems2005

    • Author(s)
      Makino, H., Tasaki, S.
    • Journal Title

      Prog.Theor.Phys. 114・5

      Pages: 929-941

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Occupation time theorems for a class of one-dimensional diffusion processes2005

    • Author(s)
      Kasahara, Y., Watanabe, S.
    • Journal Title

      Period.Math.Hungar. 50・1-2

      Pages: 175-188

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A diffusion process with a random potential consisting of two self -similar processes with different indices

    • Author(s)
      Yuki Suzuki
    • Journal Title

      Tokyo Journal of Mathematics (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A diffusion process with a random potential consisting of two self - similar processes with different indices

    • Author(s)
      Yuki, Suzuki
    • Journal Title

      Tokyo Journal of Mathematics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Energy level statistics for random operators2008

    • Author(s)
      Nariyuki Minami
    • Organizer
      Disordered Systems Random Schrodinger Operators and Random Matrices
    • Place of Presentation
      Mathematisches Forschung sinstitute Oberwolfach
    • Year and Date
      2008-03-27
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Energy level statistics for the Anderson tight binding model2007

    • Author(s)
      南 就将
    • Organizer
      ランダム作用素のスペクトルと関連する話題
    • Place of Presentation
      京都大学
    • Year and Date
      2007-11-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On distribution of eigenfunctions of random Schrodinger operators on the Bethe lattice2007

    • Author(s)
      中野 史彦
    • Organizer
      ランダム作用素のスペクトルと関連する話題
    • Place of Presentation
      京都大学
    • Year and Date
      2007-11-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Spectral statistics of systems with infinitely many components2007

    • Author(s)
      牧野 浩典
    • Organizer
      ランダム作用素のスペクトルと関連する話題
    • Place of Presentation
      京都大学
    • Year and Date
      2007-11-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Energy level statistics for the Anderson tight binding model2007

    • Author(s)
      Minami, Narivuki
    • Organizer
      Spectra of random operators and related topics
    • Place of Presentation
      Kyoto University
    • Year and Date
      2007-11-15
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On distribution of eigenfunctions of random Schrodinger operators on the Bethe lattice2007

    • Author(s)
      Fumihiko, Nakano
    • Organizer
      Spectra of random operators and related topics
    • Place of Presentation
      Kyoto University
    • Year and Date
      2007-11-15
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Spectral statistics of systems with infinitely many components2007

    • Author(s)
      Hironori, Makino
    • Organizer
      Spectra of random operators and related topics
    • Place of Presentation
      Kyoto University
    • Year and Date
      2007-11-15
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Level statistics in spin systems and Brownian motion on a sphere2007

    • Author(s)
      永尾 太郎
    • Organizer
      ランダム作用素のスペクトルと関連する話題
    • Place of Presentation
      京都大学
    • Year and Date
      2007-11-14
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Anderson localization by random vector fields2007

    • Author(s)
      上木 直昌
    • Organizer
      ランダム作用素のスペクトルと関連する話題
    • Place of Presentation
      京都大学
    • Year and Date
      2007-11-14
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Level statistics in spin systems and Brownian motion on a sphere2007

    • Author(s)
      Taro, Nagao
    • Organizer
      Spectra of random operators and related topics
    • Place of Presentation
      Kyoto University
    • Year and Date
      2007-11-14
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Anderson localization by random vector potentials2007

    • Author(s)
      Naomasa, Ueki
    • Organizer
      Spectra of random operators and related topics
    • Place of Presentation
      Kyoto University
    • Year and Date
      2007-11-14
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 樹木の空間への確率測度の導入について2007

    • Author(s)
      南 就将
    • Organizer
      日本数学会2007年度秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-22
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] On the introduction of probability measures in the space of trees2007

    • Author(s)
      Minami, Narivuki
    • Organizer
      MSJ meeting
    • Place of Presentation
      Tohoku University
    • Year and Date
      2007-09-22
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] ランダム媒質中の拡散過程の片側滞在時間2007

    • Author(s)
      笠原 勇二、渡辺 信三
    • Organizer
      日本数学会2007年度秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] ランダム媒質中のランダムウォークの片側滞在時間2007

    • Author(s)
      渡辺 信三、笠原 勇二
    • Organizer
      日本数学会2007年度秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] One-sided occupation time of diffusion processes in random media2007

    • Author(s)
      Yuii, Kasahara, Shinzo, Watanabe
    • Organizer
      MSJ meeting
    • Place of Presentation
      Tohoku University
    • Year and Date
      2007-09-21
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] One-sided occupation time of random walks in random media2007

    • Author(s)
      Shinzo, Watanabe, Yuji, Kasahara
    • Organizer
      MSJ meeting
    • Place of Presentation
      Tohoku University
    • Year and Date
      2007-09-21
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] アンダーソンモデルにおける固有値、固有関数の分布について2007

    • Author(s)
      中野 史彦
    • Organizer
      日本数学会年会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2007-03-27
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 指数の異なる2つの自己相似過程からなるポテンシャルを持つ拡散過程2007

    • Author(s)
      鈴木 由紀
    • Organizer
      日本数学会年会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2007-03-27
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Energy level statistics for random operators2007

    • Author(s)
      Minami, Nariyuki
    • Organizer
      Disordered systems : Random Schrodinger operators and random matrices
    • Place of Presentation
      Mathematischesforschungsinstitut Oberwolfach
    • Year and Date
      2007-03-27
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the distribution of eigenvalues and eigenfunctions of the Anderson model2007

    • Author(s)
      Fumihiko, Nakano
    • Organizer
      MSJ meeting
    • Place of Presentation
      Saitama University
    • Year and Date
      2007-03-27
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] A diffusion process with a random potential consisting of two self-similar processes with different indices2007

    • Author(s)
      Yuki, Suzuki
    • Organizer
      MSJ meeting
    • Place of Presentation
      Saitama University
    • Year and Date
      2007-03-27
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The energy level statistics for the Anderson tight binding model2006

    • Author(s)
      Nariyuki Minami
    • Organizer
      Spectral Theory of Random Operators and Related Fields in Probability Theory
    • Place of Presentation
      京都大学
    • Year and Date
      2006-12-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The distribution of eigenvalues in the Anderson model2006

    • Author(s)
      Fumihiko Nakano
    • Organizer
      Spectral Theory of Random Operators and Related Fields in Probability Theory
    • Place of Presentation
      京都大学
    • Year and Date
      2006-12-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Spectral statistics of sample covariance matrices2006

    • Author(s)
      Taro Nagao
    • Organizer
      Spectral Theory of Random Operators and Related Fields in Probability Theory
    • Place of Presentation
      京都大学
    • Year and Date
      2006-12-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The energy level statistics for the Anderson tight Binding model2006

    • Author(s)
      Minami, Narivuki
    • Organizer
      Spectral theory of random operators and related fields in probability theory
    • Place of Presentation
      Kyoto University
    • Year and Date
      2006-12-15
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The distribution of eigenvalues in the Anderson model2006

    • Author(s)
      Fumihiko, Nakano
    • Organizer
      Spectral theory of random operators and related fields in probability theory
    • Place of Presentation
      Kyoto University
    • Year and Date
      2006-12-15
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Spectral statistics of sample covariance matrices2006

    • Author(s)
      Taro, Nagao
    • Organizer
      Spectral theory of random operators and related fields in probability theory
    • Place of Presentation
      Kyoto University
    • Year and Date
      2006-12-01
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] A deterministic version of Palm-Khinchin formula2006

    • Author(s)
      南 就将
    • Organizer
      日本数学会2006年度年回
    • Place of Presentation
      中央大学
    • Year and Date
      2006-03-27
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] A deterministic version of Palm-Khinchin formula2006

    • Author(s)
      Minami, Narivuki
    • Organizer
      MSJ meeting
    • Place of Presentation
      Chuo University
    • Year and Date
      2006-03-27
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Central and local limit theorem for the number of vertices in a Galton-Watson tree2006

    • Author(s)
      南 就将
    • Organizer
      確率論の極限定理の研究
    • Place of Presentation
      九州大学
    • Year and Date
      2006-01-24
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Central and local limit theorems for the number of vertices in a Galton-Watson tree2006

    • Author(s)
      Minami, Narivuki
    • Organizer
      Limit theorems in probability theory
    • Place of Presentation
      Kyushu University
    • Year and Date
      2006-01-24
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] エネルギー準位統計における"unfolding"の2つの考え方について2005

    • Author(s)
      南 就将
    • Organizer
      ランダム作用素のスペクトルとその周辺
    • Place of Presentation
      筑波大学
    • Year and Date
      2005-12-06
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] アンダーソンモデルにおける局在中心の分布について2005

    • Author(s)
      中野 史彦
    • Organizer
      ランダム作用素のスペクトルとその周辺
    • Place of Presentation
      筑波大学
    • Year and Date
      2005-12-06
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Wegner estimates for certain random Schrodinger operators with magnetic fields2005

    • Author(s)
      上木 直昌
    • Organizer
      ランダム作用素のスペクトルとその周辺
    • Place of Presentation
      筑波大学
    • Year and Date
      2005-12-06
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On two notions of unfolding in energy level statistics2005

    • Author(s)
      Minami, Narivuki
    • Organizer
      Spectra of random operators and related fields
    • Place of Presentation
      University of Tsukuba
    • Year and Date
      2005-12-06
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the centers of localization in the Anderson model2005

    • Author(s)
      Fumihiko, Nakano
    • Organizer
      Spectra of random operators and related fields
    • Place of Presentation
      University of Tsukuba
    • Year and Date
      2005-12-06
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Energy level statistics for a quantum chaotic system in a magnetic field2005

    • Author(s)
      Taro, Nagao
    • Organizer
      Spectra of random operators and related fields
    • Place of Presentation
      University of Tsukuba
    • Year and Date
      2005-12-06
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Wegner estimates for certain random Schrodinger operators with magnetic fields2005

    • Author(s)
      Naomasa, Ueki
    • Organizer
      Spectra of random operators and related fiel
    • Place of Presentation
      University of Tsukuba
    • Year and Date
      2005-12-06
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 磁場中の量子カオス系のエネルギー準位統計2005

    • Author(s)
      永尾 太郎
    • Organizer
      ランダム作用素のスペクトルとその周辺
    • Place of Presentation
      筑波大学
    • Year and Date
      2005-12-05
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Central and local limit theorem for the number of vertices in a Galton-Watson tree2005

    • Author(s)
      南 就将
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-19
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] あるクラスのレヴィ過程のブラウン運動による表現2005

    • Author(s)
      笠原 勇二、渡辺 信三
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-19
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 一次元拡散過程の正側滞在時間の極限定理2005

    • Author(s)
      笠原 勇二、渡辺 信三
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-19
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Central and local limit theorems for the number of vertices in a Galton-Watson tree2005

    • Author(s)
      Minami, Narivuki
    • Organizer
      MSJ meeting
    • Place of Presentation
      Okayama University
    • Year and Date
      2005-09-19
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Representation of a class of Levy processes in terms of Brownian motion2005

    • Author(s)
      Yuii, Kasahara, Shinzo, Watanabe
    • Organizer
      MSJ meeting
    • Place of Presentation
      Okayama University
    • Year and Date
      2005-09-19
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] A limit theorem for the occupation time In the positive half-line of one-dimensional diffusion processes2005

    • Author(s)
      Yuii, Kasahara, Shinzo, Watanabe
    • Organizer
      MSJ meeting
    • Place of Presentation
      Okayama University
    • Year and Date
      2005-09-19
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] ランダムシュレーディンガー作用素のスペクトルのゆらぎについて2005

    • Author(s)
      中野 史彦
    • Organizer
      第44回実関数論、関数解析学合同シンポジウム
    • Place of Presentation
      千葉大学
    • Year and Date
      2005-08-10
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the number of vertices with a given degree in a Galton-Watson tree2005

    • Author(s)
      Minami, Narivuki
    • Organizer
      Probability and Mathematical Physics
    • Place of Presentation
      Centre de recherche Mathematique, Universite de Montreal
    • Year and Date
      2005-07-28
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the number of vertices with a given degree in a Galton-Watson tree2005

    • Author(s)
      Nariyuki Minami
    • Organizer
      Probability and Mathematical Physics
    • Place of Presentation
      Centre de recherche mathematique,Universitede Montreal
    • Year and Date
      2005-06-28
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the fluctuation of spectra of random Schrodinger operators

    • Author(s)
      Fumihiko, Nakano
    • Organizer
      44-th symposium on real and functional analysis
    • Place of Presentation
      Chiba University
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary

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Published: 2005-03-31   Modified: 2016-04-21  

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