On the chemical distance in critical percolation II
On the chemical distance in critical percolation II
复制标题
临界渗流中的化学距离 II
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Philippe Sosoe
中科院分区：
文献类型：
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作者：
M. Damron;Jack Hanson;Philippe Sosoe
我们继续我们的研究化学（图）的距离内大临界渗流集团在二维。我们证明了新的估计，其中涉及三臂概率，点到表面和点到点的距离。我们证明了同一临界渗流群中两点在Z轴上的点到点的距离具有无穷大的二阶矩。我们也给我们以前的结果比较的长度最短的交叉，最低的交叉盒的定量版本。
We continue our study of the chemical (graph) distance inside large critical percolation clusters in dimension two. We prove new estimates, which involve the three-arm probability, for the point-to-surface and point-to-point distances. We show that the point-to-point distance in Z between two points in the same critical percolation cluster has infinite second moment. We also give quantitative versions of our previous results comparing the length of the shortest crossing to that of the lowest crossing of a box.