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

Abstract

We show that the union of two or more independent uniform spanning forests (USF) on ${\mathbb{Z}}^d$ with $d\ge 3$ 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.

10 pages