| Project/Area Number |
09440079
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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) |
WATANABE Kiyoshi Kobe University, Faculty of Science, Associate Professor, 理学部, 助教授 (60091245)
TAKANO Kyoichi Kobe University, Faculty of Science, Professor, 理学部, 教授 (10011678)
FUKUYAMA Katusi Kobe University, Faculty of Science, Associate Professor, 理学部, 助教授 (60218956)
KONNO Norio Yokohama National University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (80205575)
YOSHIDA Nobuo Kyoto University, Graduate School of Science, Lecturer, 大学院・理学研究科, 講師 (40240303)
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| Project Period (FY) |
1997 – 1999
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| Keywords | Glauber dynamics / spectral gap / critical point / Ising model / percolation / shrink of contours / reinforced random walk |
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| Research Abstract |
We investigated the spectral gap of Glauber dynamics in a finite square in the low temperature case in two dimensions. This is known to have a uniform lower bound independent of the boundary condition when the temperature is higher than the critical point, and goes to zero as the size of the square goes to infinity in the low temperature case.
We obtained a sharpe lower bound of the spectral gap for the + boundary condition up to the critical point : gap(L,+)【greater than or equal】exp{-CィイD8LlogLィエD8}, where L is the size of the box. This bound is better than the existing one. It is even better than the estimate which is known only for the low enough temperature.
Further, we showed that the uniform spectral gap is equivalent to the strong mixing condition even for unbounded spin systems.
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