The number of ends in the uniform spanning tree

Vortrag von Diederik van Engelenburg

Datum: 30.11.22  Zeit: 17.15 - 18.15  Raum: ETH HG G 19.1

I will talk about a result with Tom Hutchcroft, stating that the number of ends of the uniform spanning tree (UST) is almost surely equal to the number of ends of the underlying graph in the context of recurrent stationary random rooted graphs. Together with previous results in the transient case, this completely resolves the problem of the number of ends of wired uniform spanning forest components in stationary random rooted graphs and confirms a conjecture of Aldous and Lyons (2006). Our work elaborates on work with Nathanael Berestycki, in which we relate the end-structure of the UST on recurrent graphs to potential theoretic properties of the underlying graphs.