Locality of percolation for abelian Cayley graphs
Probability
2013-12-09 v1 Group Theory
Abstract
We prove that the value of the critical probability for percolation on an abelian Cayley graph is determined by its local structure. This is a partial positive answer to a conjecture of Schramm: the function pc defined on the set of Cayley graphs of abelian groups of rank at least 2 is continuous for the Benjamini-Schramm topology. The proof involves group-theoretic tools and a new block argument.
Keywords
Cite
@article{arxiv.1312.1946,
title = {Locality of percolation for abelian Cayley graphs},
author = {Sebastien Martineau and Vincent Tassion},
journal= {arXiv preprint arXiv:1312.1946},
year = {2013}
}
Comments
28 pages with 6 figures