• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Stochastic processes in random media

Research Project

Project/Area Number 24740055
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKyoto University

Principal Investigator

Fukushima Ryoki  京都大学, 数理解析研究所, 准教授 (60527886)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords不規則媒質 / 確率過程 / 均質化 / ランダム媒質 / 高分子模型 / 中心極限定理 / アンダーソン模型 / ランダムウォーク / 国際研究者交流,ドイツ
Outline of Final Research Achievements

I have studied how disorders in materials affect the physical phenomenon. In particular, it is proved that the Anderson model, which is supposed to describe the state of an electron in disordered media, can be approximated by the homogeneous model in a certain scaling. Moreover, the scale and nature of the fluctuation caused by random disorder is determined in detail. Aside from this, a polymer model in a disordered solvent is also studied. In the limit of strong disorder, it is shown that the model can be approximated by another natural and simple model.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (32 results)

All 2016 2015 2014 2013 2012 Other

All Int'l Joint Research (3 results) Journal Article (4 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 4 results,  Open Access: 1 results) Presentation (22 results) (of which Int'l Joint Research: 4 results,  Invited: 14 results) Remarks (3 results)

  • [Int'l Joint Research] University of California Los Angels(米国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Weierstrass institute/Technical University of Berlin(Germany)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] University of Paris 7(France)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Limiting Results for the Free Energy of Directed Polymers in Random Environment with Unbounded Jumps2015

    • Author(s)
      F. Comets, R. Fukushima, S. Nakajima, N. Yoshida
    • Journal Title

      J. Stat. Phys

      Volume: Volume 161, Issue 3 Issue: 3 Pages: 577-597

    • DOI

      10.1007/s10955-015-1347-1

    • NAID

      120006644059

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Quenched large deviations for multidimensional random walk in random environment with holding times2014

    • Author(s)
      Ryoki Fukushima and Naoki Kubota
    • Journal Title

      Journal of Theoretical Probability

      Volume: 27(4) Issue: 4 Pages: 1140-1166

    • DOI

      10.1007/s10959-013-0514-z

    • Related Report
      2014 Research-status Report 2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Annealed Brownian motion in a heavy tailed Poissonian potential2013

    • Author(s)
      Ryoki Fukushima
    • Journal Title

      Annals of Probability

      Volume: 41 Issue: 5 Pages: 3462-3493

    • DOI

      10.1214/12-aop754

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] On exponential growth for a certain class of linear systems2012

    • Author(s)
      Ryoki Fukushima, Nobuo Yoshida
    • Journal Title

      Latin American Journal of Probability and Mathematical Statistics

      Volume: 9 Pages: 323-336

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Eigenvalue Fluctuations for Lattice Anderson Hamiltonians2016

    • Author(s)
      Ryoki Fukushima
    • Organizer
      2016 SIAM Conference on Mathematical Aspects of Materials Science
    • Place of Presentation
      Sheraton Society Hill Hotel, Philadelphia, Pennsylvania, USA
    • Year and Date
      2016-05-08
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] ランダム媒質における路の数え上げと最短経路に関する話題2015

    • Author(s)
      福島竜輝
    • Organizer
      IMI-RIMS共共拠点研究会
    • Place of Presentation
      九州大学
    • Year and Date
      2015-12-08
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Fluctuation of spectra in random media revisited2015

    • Author(s)
      Ryoki Fukushima
    • Organizer
      Stochastic Analysis
    • Place of Presentation
      京都大学
    • Year and Date
      2015-09-08
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Homogenization of the Anderson model2015

    • Author(s)
      Ryoki Fukushima
    • Organizer
      New Trends in Stochastic Analysis
    • Place of Presentation
      国際高等研究所(京都府木津川市)
    • Year and Date
      2015-07-09
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Limiting results for the free energy of directed polymers in random environment with unbounded jumps2015

    • Author(s)
      福島竜輝
    • Organizer
      日本数学会2015年度年会
    • Place of Presentation
      明治大学駿河台キャンパス
    • Year and Date
      2015-03-21
    • Related Report
      2014 Research-status Report
  • [Presentation] Eigenvalue fluctuations for lattice Anderson Hamiltonians2015

    • Author(s)
      福島竜輝
    • Organizer
      日本数学会2015年度年会
    • Place of Presentation
      明治大学駿河台キャンパス
    • Year and Date
      2015-03-21
    • Related Report
      2014 Research-status Report
  • [Presentation] Anderson模型の固有値の揺らぎについて2015

    • Author(s)
      福島竜輝
    • Organizer
      新潟確率論ワークショップ
    • Place of Presentation
      新潟大学駅前キャンパスときめいと
    • Year and Date
      2015-01-23
    • Related Report
      2014 Research-status Report
  • [Presentation] Homogenization and fluctuation for eigenvalues of lattice Anderson Hamiltonians2015

    • Author(s)
      Ryoki Fukushima
    • Organizer
      Spectrum of random operator and related topics
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-01-08
    • Related Report
      2014 Research-status Report
  • [Presentation] Eigenvalue fluctuations for lattice Anderson Hamiltonians2014

    • Author(s)
      Ryoki Fukushima
    • Organizer
      Stochastic analysis on large scale interacting systems
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2014-11-06
    • Related Report
      2014 Research-status Report
  • [Presentation] Biased review on the Anderson model2014

    • Author(s)
      Ryoki Fukushima
    • Organizer
      Doctorial Forum of Mathematics between Fudan and Kyoto Universities
    • Place of Presentation
      Fudan university
    • Year and Date
      2014-11-03
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] ランダムウォークの滞在時間の同時分布とLaplace原理への応用2014

    • Author(s)
      Ryoki Fukushima
    • Organizer
      確率論早春セミナー
    • Place of Presentation
      Kyoto University
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Localization of Brownian motion in random potentials2013

    • Author(s)
      Ryoki Fukushima
    • Organizer
      New directions in probability
    • Place of Presentation
      Indian Statistical Institute, Bangalore
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Brownian motion in a heavy tailed Poissonian potential2013

    • Author(s)
      Ryoki Fukushima
    • Organizer
      Pacific Rim Mathematical Association Congress 2013
    • Place of Presentation
      Shanghai Jiao Tong University
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On exponential growth of a certain linear systems2013

    • Author(s)
      Ryoki Fukushima
    • Organizer
      JSPS-DST Asian Academic Seminar 2013
    • Place of Presentation
      The University of Tokyo
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Large deviations for random walks with random holding times2013

    • Author(s)
      Ryoki Fukushima
    • Organizer
      The 12th workshop on Stochastic Analysis on Large Scale Interacting Systems
    • Place of Presentation
      The University of Tokyo
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Directed polymerの零温度極限について2013

    • Author(s)
      Ryoki Fukushima
    • Organizer
      無限粒子系、確率場の諸問題IX
    • Place of Presentation
      Nara Women's University
    • Related Report
      2013 Research-status Report
  • [Presentation] Annealed Brownian motion in a heavy tailed Poissonian potential

    • Author(s)
      Ryoki Fukushima
    • Organizer
      Workshop on Random Polymer Models and Related Problems
    • Place of Presentation
      National University of Singapore(シンガポール)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Localization for annealed Brownian motion in a heavy tailed Poissonian potential

    • Author(s)
      Ryoki Fukushima
    • Organizer
      11th workshop on Stochastic Analysis on Large Scale Interacting Systems
    • Place of Presentation
      東京大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Annealed Brownian motion in a heavy tailed Poissonian potential

    • Author(s)
      Ryoki Fukushima
    • Organizer
      Stochastic Analysis and Applications
    • Place of Presentation
      岡山大学
    • Related Report
      2012 Research-status Report
  • [Presentation] On Poisson Anderson model with polynomially decaying single site potential

    • Author(s)
      Ryoki Fukushima
    • Organizer
      スペクトル・散乱理論とその周辺
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Anderson模型に関連する話題

    • Author(s)
      Ryoki Fukushima
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] On exponential growth for a certain class of linear systems

    • Author(s)
      Ryoki Fukushima
    • Organizer
      Markov chains on graphs and related topics
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks] Researcher's website

    • URL

      http://www.kurims.kyoto-u.ac.jp/~ryoki/

    • Related Report
      2015 Annual Research Report
  • [Remarks] 所属機関の研究者個人ページ

    • URL

      http://www.kurims.kyoto-u.ac.jp/~ryoki/

    • Related Report
      2014 Research-status Report
  • [Remarks] 研究代表者のウェブページ

    • URL

      http://www.kurims.kyoto-u.ac.jp/~ryoki/

    • Related Report
      2013 Research-status Report

URL: 

Published: 2013-05-31   Modified: 2022-01-27  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi