Probability Seminar

Date Time 
Location  Speaker 
Title – click for abstract 

01/24 11:30am 
BLOC 628 
Pengfei Tang Indiana Bloomington 
Weights of wired uniform spanning forests on nonunimodular transitive graphs
Uniform spanning forests are interesting probability models that related to a lot of other areas of probability, including electrical networks, looperased 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.


01/31 11:30am 
BLOC 628 
Sarai HernandezTorres UBC 
Scaling Limits of Uniform Spanning Trees in Three Dimensions
Wilson's algorithm allows efficient sampling of the uniform spanning tree (UST) by using looperased 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, threedimensional 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 GromovHausdorfftype topology. This talk is based on joint work with Omer Angel, David Croydon, and Daisuke Shiraishi.

Please direct inquiries to
Eviatar Procaccia.