Continuidade da probabilidade de percolação em Z^2 x {0,1}

Abstract

The percolation theory began with Broadbent and Hammersley [1].One of the formulation motivations of such theory was trying to builda probabilistic model that describes the propagation of a fluid in a porousmedium. These models are built on graphs, independently assigning toeach bond (or site) the state open or closed with probability p and 1 p,respectively. The main intention of this master thesis is to study the percolation model in the graph Z2 f0, 1g introduced by Damron et al. in Absence of Site Percolation at criticality in Z2 f0, 1g (see [2]) . Our purpose in this work was to formulate the percolation model proposed in the above article, discuss the issues involved and expose the results of it.Key-words: Critical percolation, slab percolation, continuous.