Probability Seminar

Date: January 31, 2020

Time: 11:30AM - 12:30PM

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.