2003 Fiscal Year Final Research Report Summary
MATEMATICAL ANALYSIS OF INFINITE DIMENSIONAL STOCHASTIC MODELS
| Project/Area Number |
13640103
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
SHIGA Tokuzo TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Professor, 大学院・理工学研究科, 教授 (60025418)
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| Co-Investigator(Kenkyū-buntansha) |
角 大輝 東京工業大学, 大学院・理工学研究科, 助手 (40313324)
SHIRAI Tomoyuki Kanazawa University, Faculty of Science, Associate Professor, 理学部, 助教授 (70302932)
MORITA Takehiko Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00192782)
NOMURA Yuji TOKYO INSTITUTE OF TECHNOLOGY, Graduate School of Science and Engineering, Assistant Professor, 大学院・理工学研究科, 助手 (40282818)
HARA Takashi Nagoya University, Graduate School of Mathematics, Associate Professor, 多元数理研究科, 助教授 (20228620)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Strong Disorder / Anderson Localization / Fermion Random Field / Critical Phenomena / アンダーソン局在 / フェルミオン確率場 / 臨界現象 |
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| Research Abstract |
We performed this research project on "Mathematical Analysis of Infinite Dimensional Stochastic Models", and obtained the following results.
1.Asymptotics of Lyapunov exponent of Anderson model : It is established that the discrete heat equation with space-time white noise potential over the discrete Euclidean space, so salled "Parabolic Anderson model" has a Lyapunov exponent exhibiting the exponential order of the solution, which is independent of initial conditions. Morever we developed asymptotic analysis of the exponent with respect to the coupling constant and obtained precise asymptotic formula.
2.Directed Polymers in Random environment : The theory of directed polymers in random environments is still underdeveloping, particularly in low dimensional cases. We established equivalence of local property of the sample path and some decay order of the random partition functions.
3.One of co-workers of this project investigated spectrum structure of random Schroedinger operator over line graph and proved "Anderson localization", another one investigated ergodic properties of the shift dynamics associated with fermion random fields. The other one contributed to the rigorous theory of critical phenomena for stochastic statistical mechanics in establishing presice asymptotic order of two point functions in self-avoiding random walk models and related models.
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