Amenability criterions and critical probabilities in percolation
arXiv:1403.0909
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.
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