RUSSO-SEYMOUR-WELSH ON PERCOLATION MODELS

Abstract

In this thesis, we summarize the recent Russo-Seymour-Welsh (RSW) results and the application of the RSW result to evaluate crossing probabilities at criticality for both the Voronoi percolation and random cluster model. The statements and proofs follow closely the individual work of Tassion and the joint work of Duminil-Copin and Tassion with additional remarks and details to make the proofs more accessible.