Percolação auto-destrutiva

Abstract

The self-destructive percolation model, introduced by van den Berg and Brower, is defined as follows: consider the ordinary percolation model parameter p > pc. Remove the infinite occupied cluster and give each vertex (or, for bond percolation, each edge) that is vacant anextra chance d to became occupied. Let dc(p) be the minimal value of d needed to reintroduce an infinite occupied cluster. The main goal of this dissertation is to study the value of dc(p) when p > pc is near thecritical point for bidimensional graphs, like the square lattice and the binary tree, among others. We will study the articles "Self-destructive percolation" written by van den Berg and Brower, and "Linear lower bounds for dc(p) for a class of 2D self-destructive percolation models"written by van den Berg and de Lima.