Homogenization via sprinkling

Abstract

We show that a superposition of an $\epsilon$-Bernoulli bond percolation and any everywhere percolating subgraph of ${\mathbb{Z}}^d$, $d\ge 2$, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli percolation. This result, which confirms a conjecture of the first author together with Häggström and Schramm (2000), is mainly motivated by obtaining finite volume characterizations of uniqueness for general percolation processes.

11 pages

References in corpus (1)

• Percolation and local isoperimetric inequalities