Is the critical percolation probability local?
Probability
2009-01-30 v1 Group Theory
Abstract
We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. This is a special case of a conjecture due to O. Schramm on the locality of p_c. We also prove a finite analogue of the conjecture for expander graphs.
Keywords
Cite
@article{arxiv.0901.4616,
title = {Is the critical percolation probability local?},
author = {Itai Benjamini and Asaf Nachmias and Yuval Peres},
journal= {arXiv preprint arXiv:0901.4616},
year = {2009}
}
Comments
9 pages