2009 Fiscal Year Final Research Report
Stochastic analysis on large scale interacting systems
| Project/Area Number |
18204007
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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 | The University of Tokyo |
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Principal Investigator |
FUNAKI Tadahisa The University of Tokyo, 大学院・数理科学研究科, 教授 (60112174)
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| Co-Investigator(Kenkyū-buntansha) |
OSADA Hirofumi 九州大学, 大学院・数理学研究院, 教授 (20177207)
WEISS Georg 東京大学, 大学院・数理科学研究科, 准教授 (30282817)
OTOBE Yoshiki 信州大学, 理学部, 講師 (30334882)
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| Co-Investigator(Renkei-kenkyūsha) |
MIMURA Masayasu 明治大学, 理工学部, 教授 (50068128)
HIGUCHI Yasunari 神戸大学, 理学部, 教授 (60112075)
TANEMURA Hideki 千葉大学, 理学部, 教授 (40217162)
KUMAGAI Takashi 京都大学, 大学院・理学研究科, 教授 (90234509)
YOSHIDA Nobuo 京都大学, 大学院・理学研究科, 准教授 (40240303)
CHIYONOBU Taizo 関西学院大学, 理工学部, 教授 (50197638)
HANDA Kenji 佐賀大学, 理工学部, 准教授 (10238214)
SUGIURA Makoto 琉球大学, 理学部, 准教授 (70252228)
NISHIKAWA Takao 日本大学, 理工学部, 講師 (10386005)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 確率論 / 解析学 / 統計力学 / 応用数学 / 数理物理 / 関数方程式論 |
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| Research Abstract |
We have studied large scale interacting systems related to the interface model and the theory of random matrices, based on the stochastic analysis and the theory of nonlinear partial differential equations. In particular, concerning the interface model on a wall or with a pinning effect, we have made a precise analysis and determined the scaling limit when the corresponding large deviation rate functional admits plural minimizers, and moreover, established the hydrodynamic limit for an evolutional model of two dimensional Young diagrams. As a dynamic model in the theory of random matrices, we have investigated the system of Ginibre interacting Brownian particles and found an outstanding property, that is, the sub-diffusive behavior of a tagged particle in this system.
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