The Russo-Seymour-Welsh Theory for Dependent Percolation Models and its Applications

The Russo-Seymour-Welsh Theory for Dependent Percolation Models and its Applications

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Hugo Duminil-Copin, IHES
TBD

In this third talk, we wish to present some of the mathematical study of critical percolation on a two-dimensional lattice. A key tool in analysing such models is a famous theorem, dating back to Russo and Seymour-Welsh (RSW) in 1978, dealing with crossing probabilities of rectangles. While the scope of the RSW theory remained limited for thirty years to a special model called Bernoulli percolation, the field progressed tremendously in the last ten years. The RSW theory has been extended to a variety of models, creating an explosion of results about dependent percolation models. We will present some of the recent developments and the new applications of the RSW theory.