# Student Probability Seminar

#### Topics in 2D Percolation

Speaker: Reza Gheissari

Location: Warren Weaver Hall 1314

Date: Wednesday, September 20, 2017, 10 a.m.

Synopsis:

Independent percolation on $\mathbb Z^d$ is one of the most well-studied models in statistical physics, exhibiting a rich phase transition that has been extensively explored. We will introduce bond percolation in 2D and understand some of its properties along with the techniques used to study its phase transition. Specifically, we will show that the infinite cluster is almost surely unique and develop the RSW theory of crossing probabilities of rectangles with bounded aspect ratio. The goal will be to give most of the steps necessary to identifying the critical point as $p_c=\frac 12$ on $\mathbb Z^2$ and showing that there is a.s. no infinite cluster at $p=p_c$.