Densidade crítica no modelo de percolação em rede de Bethe não-homogênea

Abstract

In this work we deal with an inhomogeneous Bethe lattice percolation model where the probability of an edge in level n is open changes according as n. This model can be appropriate to the case where the media changes its density in a systematic way, such as the proliferation of insects that depends on the temperature and humidity, which fluctuates between day and night. We consider the case where the density p(·) follows a function of the distance l(.) from the origin, given by a sinusoid function p(·) = p + (1 - p)|sin(l(.))|. For this model we present results of Monte-Carlo simulation showing the behavior of the probability of percolation with a second-order phase transition, but we present too a formal proof that the density is non trivial, with the mathematical expression to compute the percolation threshold.