Michael DamronGeorgia TechJack HansonGeorgia Tech, CUNYPhilippe SosoeHarvard University CMSA
Publications of CMSA of Harvardmathscidoc:1702.38046
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 2 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.
@inproceedings{michaelon,
title={On the Chemical Distance in Critical Percolation II},
author={Michael Damron, Jack Hanson, and Philippe Sosoe},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207034201404168246},
}
Michael Damron, Jack Hanson, and Philippe Sosoe. On the Chemical Distance in Critical Percolation II. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207034201404168246.