The cluster expansion and combinatorics

Combinatorics Seminar
Friday, September 9, 2022 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 202
Will Perkins – Georgia Institute of Technology –
Anton Bernshteyn

The cluster expansion is a classical tool from statistical physics used to understand systems of weakly interacting particles in the high temperature regime of statistical physics models.  It can also be a very useful tool in probabilistic, extremal, and enumerative combinatorics and in the study of large deviations in probability theory.  I will give an introduction to the cluster expansion, present some examples of combinatorial applications, and try to provide some intuition about when the cluster expansion should or should not be a useful tool for a particular problem.