| 渗流簇中鞅中心极限定理的收敛速度 |
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| 作者姓名： | 姜建平 张三国 郭田德 |
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| 作者单位： | 中国科学院研究生院数学科学学院, 北京 100049 |
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| 基金项目： | Supported by Knowledge Innovation Program of the Chinese Academy of Sciences(kjcx-yw-s7), the National Natural Science Foundation of China (10831006) and Presidential Foundation of GUCAS(O85101BM03) |
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| 摘 要： | 考虑定义在Zd上参数为p的边渗流模型.假设Kn为 -n,n]d中开簇的个数,研究了关于Kn的鞅中心定理的收敛速度.一般情况下,经鞅中心极限定理的最好收敛速度是O(n-d/2),而我们的结果为Pp((Kn-Ep(Kn))/(Varp(Kn))) ≤x =x∫-∞(1/(2π)) e(-y2)/2dy+o(n-d/2 +ε0)对任意的实数x都成立,这里ε0是区间 0, d/2 上的任意实数.据我们所知,这是关于渗流中心极限定理收敛速度的第一结果.
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| 关 键 词： | 渗流 鞅 中心极限定理 收敛速度 |
| 收稿时间： | 2010-03-09 |
| 修稿时间： | 2010-04-16 |
Convergence rate in a martingale CLT for percolation clusters |
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| Authors: | JIANG Jian-Ping ZHANG San-Guo GUO Tian-De |
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| Institution: | School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | Consider bond percolation on Zd with parameter p. Let Kn be the number of open clusters in -n,n]d. We investigate the convergence rate in the martingaleCLT for Kn. Generally, the best convergence rate for classicalmartingale CLT is O(n-d/2), and our result is Pp((Kn-Ep(Kn))/(Varp(Kn))) ≤x =x∫-∞(1/(2π)) e(-y2)/2dy+o(n-d/2 +ε0) for all x, where ε0 is any constant real number in 0, d/2 . As far as we know, this is the first convergence rate in CLTs for percolation. |
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| Keywords: | percolation martingale central limit theorem rate of convergence |
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