2002 Fiscal Year Final Research Report Summary
Research on the formation and fluctuation of random shapes in mathematical models of statistical mechanics
| Project/Area Number |
12440027
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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 | KOBE UNIVERSITY |
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Principal Investigator |
HIGUCHI Yasunari Kobe University Faculty of Science Professor, 理学部, 教授 (60112075)
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| Co-Investigator(Kenkyū-buntansha) |
NAKANISHI Yasutaka Kobe University Faculty of Science Professor, 理学部, 教授 (70183514)
MIYAKAWA Tetsuro Kobe University Faculty of Science Professor, 理学部, 教授 (10033929)
FUKUYAMA Katsushi Kobe University Faculty of Science Professor, 理学部, 教授 (60218956)
MURAI Joushin Okayama University Graduate School of Humanities and Social sciences Assistant, 大学院・文化科学研究科, 助手 (00294447)
YAMAZAKI Tadashi Kobe University Faculty of Science Professor, 理学部, 教授 (30011696)
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| Project Period (FY) |
2000 – 2002
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| Keywords | Widom-Rowlinson model / phase separation / central limit theorem / local limit theorem / Wulff shape / phase structure / translation invariance / Gibbs states |
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| Research Abstract |
1. We found a new proof of the fact that there are only two extremal Gibbs states for the two dimensional Ising model based on the percolation argument. As an application of this new method, we proved that there are only two extremal points of translationally invariant Gibbs states for the two dimensional Widom-Rowlinson model for sufficiently low temperatures.
2. We gave an estimate of the speed of convergence for the time constant of the first passage Ising percolation for temperatures above the critical point.
3. We proved a Dobrushin-Hryniv type limit theorem for the two-dimensional Widom-Rowlinson model. The conditions for the result to hold are a little relaxed.
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