The local limit of uniform spanning trees

Asaf Nachmias; Yuval Peres

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arXiv · 2011.08833

The local limit of uniform spanning trees

Asaf Nachmias·Yuval Peres

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Abstract

We show that the local limit of the uniform spanning tree on any finite, simple, connected, regular graph sequence with degree tending to infinity is the Poisson(1) branching process conditioned to survive forever. An extension to "almost" regular graphs and a quenched version are also given.

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Asaf Nachmias, Yuval Peres. 2020-11-17. The local limit of uniform spanning trees. https://arxiv.org/abs/2011.08833

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