| 上临界渗流转角问题研究(英文) |
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| 作者姓名： | 孔瑞远 郭田德 |
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| 作者单位： | 中国科学院大学数学科学学院, 北京 100049 |
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| 基金项目： | Supported by National Natural Science Foundation of China(71271204,11331012,and 11101420) |
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| 摘 要： | 研究二维上临界边渗流,主要关注开路旋转角度的一些性质.假设从原点到边长为n的盒子边界存在一条开路,在此条件下,证明这些路的旋转角度的最大值满足大数律.此外,还证明对于任意δ0,当n充分大时,大概率地有相邻左右贯穿开路的2个相邻接触点的距离小于log1+δn.
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| 关 键 词： | 转角 贯穿路 大数律 接触点 |
| 收稿时间： | 2012-12-04 |
| 修稿时间： | 2013-04-24 |
A note on winding angles for supercritical percolation |
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| Authors: | KONG Ruiyuan GUO Tiande |
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| Institution: | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | This paper studies the supercritical Bernoulli bond percolation in two dimensions, focusing on properties of the winding angles of open paths. Under the condition that there exists an open path from the origin to the boundary of box B(n), we prove that a law of large numbers holds for the maximum of such paths' winding angles. Moreover, we show that for any δ>0, there is a high probability that the distance between two adjacent contact points in two neighboring "innermost" left-right crossings is less than log1+δn for sufficiently large n. |
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| Keywords: | winding angle crossing law of large numbers contact point |
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