Weights of uniform spanning forests on nonunimodular transitive graphs
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Publication:2076634
DOI10.1214/21-EJP709zbMATH Open1492.60294arXiv1908.09889OpenAlexW2970227179MaRDI QIDQ2076634
Author name not available (Why is that?)
Publication date: 22 February 2022
Published in: (Search for Journal in Brave)
Abstract: Considering the wired uniform spanning forest on a nonunimodular transitive graph, we show that almost surely each tree of the wired uniform spanning forest is light. More generally we study the tilted volumes for the trees in the wired uniform spanning forest. Regarding the free uniform spanning forest, we consider several families of nonunimodular transitive graphs. We show that the free uniform spanning forest is the same as the wired one on Diestel--Leader graphs. For grandparent graphs, we show that the free uniform spanning forest is connected and has branching number bigger than one. We also show that each tree of the free uniform spanning forest is heavy and has branching number bigger than one on a free product of a nonunimodular transitive graph with one edge when the free uniform spanning forest is not the same as the wired.
Full work available at URL: https://arxiv.org/abs/1908.09889
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