UBC Probability Seminar: Sarai Hernandez Torres (Online)

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 high dimensions. However, three-dimensional scaling limits are far from understood. This talk is about recent advances in this problem when we describe the UST as a metric measure space. Our main result is on the existence of sub-sequential scaling limits and convergence under dyadic scalings with respect to a Gromov-Hausdorff-type topology. We will also discuss some properties of the limit tree. This is joint work with Omer Angel, David Croydon, and Daisuke Shiraishi.