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

Eleanor Archer; Asaf Nachmias; Matan Shalev; Pengfei Tang

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

Probability 2023-11-16 v1

Authors: Eleanor Archer , Asaf Nachmias , Matan Shalev , Pengfei Tang

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.

Keywords

uniform spanning forest transient graph bernoulli percolation zd lattice independent unions

Cite

@article{arxiv.2311.09183,
  title  = {The union of independent USFs on $\mathbb{Z}^d$ is transient},
  author = {Eleanor Archer and Asaf Nachmias and Matan Shalev and Pengfei Tang},
  journal= {arXiv preprint arXiv:2311.09183},
  year   = {2023}
}

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10 pages

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

Abstract

Keywords

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