Scaling limit of high-dimensional random spanning trees

A spanning tree of a finite connected graph G is a connected
subgraph of G that includes every vertex and contains no cycles. In this
talk we will consider uniformly drawn spanning trees of high-dimensional
graphs, and explain why, under appropriate rescaling, they converge in
distribution as metric-measure spaces to Aldous’ Brownian CRT . Our
result extends an earlier result of Peres and Revelle (2004) who
previously showed a form of finite-dimensional convergence. If time
permits, we may also discuss scaling limits of random spanning trees
with non-uniform laws. Based on joint works with Asaf Nachmias and Matan Shalev.

• Speaker: Eleanor Archer (Paris)
• Tuesday 28 May 2024, 14:14–15:15
• Venue: MR12.
• Series: Probability; organiser: Perla Sousi.