Amenability criterions and critical probabilities in percolation
Group Theory
2018-12-31 v2 Probability
Abstract
A new proof of a Theorem of Nagnibeda and Pak on critical probabilities is given. The distinctive feature is to use a criterion of Folner which has been largely (and inexplicably) forgotten.
Cite
@article{arxiv.1403.0909,
title = {Amenability criterions and critical probabilities in percolation},
author = {Antoine Gournay},
journal= {arXiv preprint arXiv:1403.0909},
year = {2018}
}
Comments
10 pages. The proof of Theorem 4.1 in the previous version contains a mistake; the validity of the corresponding statement is open (see question 5.5 of the current version). The current Theorem 4.1 gives Folner's original criterion, while Theorem 5.4 shows it can in a weaker guise be applied to actions