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Infinite-Dimensional Stochastic approach to Geometrical Objects

Research Project

Project/Area Number 17540124
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 InstitutionSaga University

Principal Investigator

MITOMA Itaru  Saga University, Mathematics, Professor, 理工学部, 教授 (40112289)

Co-Investigator(Kenkyū-buntansha) OGURA Yukio  Saga University, Mathematics, Professor, 理工学部, 教授 (00037847)
TANIGUCHI Setsuo  Kyushu University, Mathematics, Professor, 大学院・数理学研究院, 教授 (70155208)
ICHIKAWA Takashi  Saga University, Mathematics, Professor, 理工学部, 教授 (20201923)
AIDA Shigeki  Osaka University, Mathematics, Professor, 大学院・基礎工学研究科, 教授 (90222455)
HANDA Kenji  Saga University, Mathematics, Associate Professor, 理工学部, 助教授 (10238214)
Project Period (FY) 2005 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2006: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2005: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsChern-Simons integral / Wiener space / Wilson line / Holonomy / Topological invariant / Topological field theory / Superstring / Wiener空間 / リンク不変量 / 漸近展開 / チャーン・サイモンズ理論 / ウィルソンループ / リンク数 / ファインマン積分
Research Abstract

We,(Mitoma-Nishikawa),gave a mathematical definition for perturbative 1-loop approximation of the Chern-Simons integral with respect to the Wilson lines in an abstract Wiener space setting and proved the asymptotic expansion theorem. Further we calculate the copefficients for 3-dimensional surface and obtained link invariants. The result is now prepared for submission. We,(Albeverio-Mitoma),gave mathematical definitions for finite part and asymptotic estimate for infinite part of perturbative Chern-Simons integral via Wiener space. The result is appeared in SFB,611 in Bonn University.

Report

(3 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • Research Products

    (23 results)

All 2007 2006 2005 Other

All Journal Article (22 results) Book (1 results)

  • [Journal Article] Asymptotic Expansion of Perturbative Chern-Simons Theory Via Wiener Space2007

    • Author(s)
      S.Albeverio, I.Mitoma
    • Journal Title

      SFB 611, Bonn University No. 322

      Pages: 50-50

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic Expansion of Perturbative Chern-Simons Theory via Wiener Space2007

    • Author(s)
      Sergio Albeverio, Itaru Mitoma
    • Journal Title

      SFB 611, Bonn University No. 322

      Pages: 50-50

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic Expansion of Perturbative Chern-Simons Theory via Wiener Space2007

    • Author(s)
      Sergio Albeverio, Itaru Mitoma
    • Journal Title

      SFB611, Bonn University 322

      Pages: 50-50

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On a Choquet theorem for random upper semicontinuous functions2006

    • Author(s)
      Yukio Ogura
    • Journal Title

      Soft Method for Integrated Uncertainty Modelling

      Pages: 145-151

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Strong law of large numbers for independent fuzzy set-valued random variables2006

    • Author(s)
      Shoumei Li, Yukio Ogura
    • Journal Title

      Fuzzy Sets and Systems 157

      Pages: 2569-2578

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On the Quadratic Wiener Functional Associated with the Malliavin Derivative of the Square Norm of Brownian Sample Path on Interval2006

    • Author(s)
      Setsuo Taniguchi
    • Journal Title

      Electron. Comm. Probab. 11

      Pages: 1-10

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Brownian sheet and reflectionless potentials2006

    • Author(s)
      Setsuo Taniguchi
    • Journal Title

      Stoch. Pro. Appl. 116 (2)

      Pages: 293-309

    • NAID

      120000981479

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A family of Schottky groups arising from the hypergeometric equation2006

    • Author(s)
      Takashi Ichikawa, Masaaki Yoshida
    • Journal Title

      Proc. of Amer. Math. Soc 134 (8)

      Pages: 2271-2280

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A note on random upper semicontinuous functions2006

    • Author(s)
      Hung T.Nguen, Yukio Ogura, Santi Tasena, Hien Tran
    • Journal Title

      Soft Method for Integrated Uncertainty Modelling

      Pages: 129-135

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Strong law of large numbers for independent fuzzy set-valued random variables2006

    • Author(s)
      Shoumei Li, Yukio Ogura
    • Journal Title

      Fuzzy Sets and Systems Vol. 157

      Pages: 2569-2578

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On the Quadratic Wiener Functional Associated with the Malliavin Derivative of the Square Norm of Brownian Sample Path on Interval2006

    • Author(s)
      S.Taniguchi
    • Journal Title

      Electron. Comm. Probab. 11

      Pages: 1-10

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Brownian sheet and reflectionless potentials2006

    • Author(s)
      S.Taniguchi
    • Journal Title

      Stoch. Pro. Appl. 116 (2)

      Pages: 293-309

    • NAID

      120000981479

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A family of Schottky groups arising from the hypergeometric equation2006

    • Author(s)
      Takashi Ichikawa, Masaaki Yoshida
    • Journal Title

      Proc. of Amer. Math. Soc. 134 (8)

      Pages: 2271-2280

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Strong law of large numbers for independent fuzzy set-valued random variables2006

    • Author(s)
      Shoumei Li, Yukio Ogura
    • Journal Title

      Fuzzy Sets and System 157

      Pages: 2569-2578

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Brownian sheet and reflectionless potientials2006

    • Author(s)
      Setsuo Taniguchi
    • Journal Title

      Stoch. Pro. Appl. 116(2)

      Pages: 293-309

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A family of Schottky groups arising from the hypergeometric equation,2006

    • Author(s)
      Takashi Ichikawa, Masaaki Yoshida
    • Journal Title

      Proc. of Amer. Math. Soc. 134 (8)

      Pages: 2271-2280

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Sampling formulae for symmetric selection2005

    • Author(s)
      Kenji Handa
    • Journal Title

      Electron. Commun. Probab. 10

      Pages: 223-234

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On Some Metrics Compatible with the Fell-Matheron Topology

    • Author(s)
      Yukio Ogura
    • Journal Title

      Internat. Jour. Approximate Reasoning (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On a class of one-dimensional Markov processes with continuous paths

    • Author(s)
      Nubuyuki Ikeda, Yukio Ogura
    • Journal Title

      "Stochastic Analysis and Partial Differential Equations" AMS Comtemp. Math. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The heat semigroup and kernel associated with certain non-commutative harmonic oscillators

    • Author(s)
      S.Taniguchi
    • Journal Title

      Kyushu Jour. Math. (to appear)

    • NAID

      110006647914

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On the Jacobi field approach to stochastic oscillatory integrals with quadratic phase functions

    • Author(s)
      S.Taniguchi
    • Journal Title

      Kyushu Jour. of Math. (to appear)

    • NAID

      130000063190

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On a class of one-dimensional Markov processes with continuous paths

    • Author(s)
      Nobuyuki Ikeda, Yukio Ogura
    • Journal Title

      "Stochastic Analysis and Prartial Differential Equations" AMS Comtemp. Math. (To appear)

    • Related Report
      2006 Annual Research Report
  • [Book] 確率論入門I2006

    • Author(s)
      池田信行, 小倉幸雄, 高橋陽一郎, 眞鍋昭治郎
    • Publisher
      培風館
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary

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Published: 2005-04-01   Modified: 2016-04-21  

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