Uniform Spanning Trees and the Burton-Pemantle Theorem

Abstract

This talk will review the uniform spanning tree model on general graphs, concentrating on its determinantal nature. In particular, I will review the celebrated Burton-Pemantle theorem, a fundamental and unexpected result which showed that its edge set is a determinantal point process, almost 150 years after Kirchoff first showed the basic version of this result for individual edges. Recent work on random matrix theory connected to electrical networks should shed some light on another method of analyzing this celebrated result, which I will discuss.