Minhao Bai, Rutgers University

Abstract

In this talk I'll briefly introduce percolation theory, which is in the intersection of probability theory, network theory and statistical mechanics. It's raised from this question: If we 2-color all vertices of a lattice independently, when will it contain an infinite cluster? What if we are coloring all edges instead? The answer is that there exists a threshold for this to happen. I'll introduce the basic techniques in this area and show some of the thresholds when time permits.