| Project/Area Number |
11440029
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Graduate School of Mathematics, Nagoya University |
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Principal Investigator |
OSADA Hirofumi Nagoya University, Graduate school of mathemati professor, 大学院・多元数理科学研究科, 教授 (20177207)
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| Co-Investigator(Kenkyū-buntansha) |
LIANG Song Nagoya University, Graduate school of mathemati Assistant, 大学院・多元数理科学研究科, 助手 (60324399)
ISHIGE Kazuhiro Nagoya University, Graduate school of mathemati Associate Professor, 大学院・多元数理科学研究科, 助教授 (90272020)
HATTORI Tetsaya Nagoya University, Graduate school of mathemati Associate Professor, 大学院・多元数理科学研究科, 助教授 (10180902)
UEMURA Hideaki Aichi Univ.of Education, Dops.of Math, Scien AP., 教育学部, 助教授 (30203483)
SHINODA Masato Nara Women's University, Facs Science, Leeture, 理学部, 講師 (50271044)
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| Project Period (FY) |
1999 – 2002
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| Keywords | diffusion processes / Dirichlet forms / Fractal / Sierpinski Carpet / Iso perimetic inequality / Marka process / Random Matrix / determinantal randomu-point field |
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| Research Abstract |
The purpose of this research is by using a method the head investigator developed to construct diffusion on infinitely ramified fractals such as Sierpinski carpets, configuration spaces and path spaces. These space are outstandingly of interest and hard to construct nice diffusion processes by using usual methods.
In case of fractals we construct diffusion processes which are self-similar and reversible with respect to the Hausdroff measures on the fractals. We used here the method of singular time change. As for random fractals we introduce "bubbles" which has a statistical self-similarity. Although we construct diffusion by using our general theory based on Dirichlet form approach, the detailed investigation of them are future's themes.
Some new facts about percolation on fractal lattices are discovered. As for infinite particle systems, we construct diffusions whose stationary measures are so-called "determinantal random point fields". This class of probability measures is very interesting because they are related to random matrix theory and special functions such as Airy functions. This class of probability measures Are different from Ruelle's class Gibbs measures and, I suppose, will be studied extensively in future. As for path spaces we construct diffusions whose invariant measures are Gibbs measures on path spaces, which we also constructed in a course of this research.
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