2 papers
math.PR2023
The number of ends in the uniform spanning tree for recurrent unimodular random graphs
Diederik van Engelenburg, Tom Hutchcroft
We prove that if a unimodular random rooted graph is recurrent, the number of ends of its uniform spanning tree is almost surely equal to the number of ends of the graph. Together…
math.PR2021
Harnack inequality and one-endedness of UST on reversible random graphs
Nathanaël Berestycki, Diederik van Engelenburg
We prove that for recurrent, reversible graphs, the following conditions are equivalent: (a) existence and uniqueness of the potential kernel, (b) existence and uniqueness of harmo…