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arXiv · 2311.09183

The union of independent USFs on $\mathbb{Z}^d$ is transient

Eleanor Archer·Asaf Nachmias·Matan Shalev·Pengfei Tang
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Abstract

We show that the union of two or more independent uniform spanning forests (USF) on $\mathbb{Z}^d$ with $d\geq 3$ almost surely forms a connected transient graph. In fact, this also holds when taking the union of a deterministic everywhere percolating set and an independent $\epsilon$-Bernoulli percolation on a single USF sample.

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Eleanor Archer, Asaf Nachmias, Matan Shalev, Pengfei Tang. 2023-11-15. The union of independent USFs on $\mathbb{Z}^d$ is transient. https://arxiv.org/abs/2311.09183

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