Random Matrix Statistics in the Uniform Spanning Tree

Explore a 51-minute lecture on random matrix statistics in uniform spanning trees presented by Nathanael Berestycki from the University of Vienna at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Delve into the analysis of wired uniform spanning trees in simply connected domains, focusing on the n arms event and its connection to random matrix theory. Discover how the boundary positions of tree branches relate to the circular orthogonal ensemble's eigenvalue distribution and how Dyson Brownian motion drives the Loewner evolution describing these curves. Examine the differences in analysis between odd and even cases, including Fomin's determinantal formula and the role of loop measure terms in topological information. Gain insights into the singular winding of curves near the origin and expand your understanding of statistical mechanics and discrete geometry.