High order correlation inequalities for random spanning trees
| Speaker: | David Wagner |
|---|---|
| Affiliation: | University of Waterloo |
| Room: | Mathematics and Computer Building (MC) 5479 |
Abstract:
A (finite) point process is just a probability measure on the set of all subsets of a finite set. Ursell functions occur naturally in statistical mechanics, and for point processes they have a very simple form. Inequalities for Ursell functions provide correlation inequalities for various occupation probabilities: covariances are the simplest nontrivial case. So-called "determinantal" point processes have some special properties, and for these the Ursell functions are especially pleasant. The Burton-Pemantle Theorem shows that choosing a random spanning tree of a graph is a determinantal point process. In this case, by considering harmonic functions on graphs we can determine the sign of Ursell functions in a variety of interesting cases. This is in part joint work with Wenbo Gao.