Percolação crítica em lajes

Abstract

Percolation was introduced in mathematical literature in(BROADBENT;HAMMERSLEY,1957) through the formulation of a simple stochastic model to understand the phenomenon off luid transport through a porous medium.The main objective of this dissertation is to understand the Bernoulli percolation model of edges on slabs, which are graph softhe form Z2×{0,...,k}. Precisely, wepresent the central result contained in (DUMINIL; SIDORAVICIUS; TASSION, 2016), which demonstrates the almost sure absence of ani nfinite cluster at th ecritical point for the Bernoulli percolatio nmodel of edges on slabs. We also presente the classical and necessary tools for the study of Bernoulli percolation on these graphs, suchas the FKG Inequality, theorems on the existence of the infinite cluster in the supercritical phase, as well as it suniqueness. Keywords: Graph percolation, critical point, absence of infinite cluster, FKG Inequality.