收稿日期: 2012-12-04
修回日期: 2013-04-24
网络出版日期: 2014-03-15
基金资助
Supported by National Natural Science Foundation of China(71271204,11331012,and 11101420)
A note on winding angles for supercritical percolation
Received date: 2012-12-04
Revised date: 2013-04-24
Online published: 2014-03-15
Supported by
Supported by National Natural Science Foundation of China(71271204,11331012,and 11101420)
孔瑞远 , 郭田德 . 上临界渗流转角问题研究[J]. 中国科学院大学学报, 2014 , 31(2) : 145 -154 . DOI: 10.7523/jssn.2095-6134.2014.02.001
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.
Key words： winding angle; crossing; law of large numbers; contact point
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