Monotonicity of the probability of percolation for Bernoulli random fields on periodic graphs

Abstract

In this work, the problem of percolation of the Bernoulli random field on periodic graphs Lambda of an arbitrary dimension D is studied. We have proved the presence of a very important property of the monotone increase with respect to each of concentrations of the field for the probability of percolation Q[x|c] of Bernoulli random fields