A note on percolation

Abstract

An improvement of Harris' theorem on percolation is obtained; it implies relations between critical points of matching graphs of the type of the one stated by Essam and Sykes. As another consequence, it is proved that the percolation probability, as a function of the probability of occupation of a given site, is infinitely differentiable, except at most in the critical point. © 1978 Springer-Verlag.