Skip to content
Texas A&M University
Mathematics

Probability Seminar

Spring 2020

 

Date:January 24, 2020
Time:11:30am
Location:BLOC 628
Speaker:Pengfei Tang, Indiana Bloomington
Title:Weights of wired uniform spanning forests on nonunimodular transitive graphs
Abstract:Uniform spanning forests are interesting probability models that related to a lot of other areas of probability, including electrical networks, loop-erased random walk, the Abelian sandpile models. In this talk, we will focus on the geometry of wired uniform spanning forest on nonunimodular transitive graphs. In particular, we will show that almost surely every tree of the wired uniform spanning forests is light. More generally, tilted volumes for the trees in WUSF will be discussed.

Date:January 31, 2020
Time:11:30am
Location:BLOC 628
Speaker:Sarai Hernandez-Torres, UBC
Title:Scaling Limits of Uniform Spanning Trees in Three Dimensions
Abstract:Wilson's algorithm allows efficient sampling of the uniform spanning tree (UST) by using loop-erased random walks. This connection gives a tractable method to study the UST. The strategy has been fruitful for scaling limits of the UST in the planar case and in high dimensions. However, three-dimensional scaling limits are far from understood. This talk is about recent advances on this problem. First, we will show that rescaled subtrees of the UST in three dimensions converge to a limiting object. Then we will describe the UST as a metric measure space. We will show that the scaling limit of the UST exists with respect to a Gromov-Hausdorff-type topology. This talk is based on joint work with Omer Angel, David Croydon, and Daisuke Shiraishi.