Neighboring clusters in Bernoulli percolation
概率论
2016-08-14 v1
摘要
We consider Bernoulli percolation on a locally finite quasi-transitive unimodular graph and prove that two infinite clusters cannot have infinitely many pairs of vertices at distance 1 from one another or, in other words, that such graphs exhibit ``cluster repulsion.'' This partially answers a question of H\"{a}ggstr\"{o}m, Peres and Schonmann.
引用
@article{arxiv.math/0702873,
title = {Neighboring clusters in Bernoulli percolation},
author = {Adám Timár},
journal= {arXiv preprint arXiv:math/0702873},
year = {2016}
}
备注
Published at http://dx.doi.org/10.1214/009117906000000485 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)