2015/05/22 by Itai Benjamini, Benjamini, Itai, Vincent Tassion +1
Mathematics · #05C80 (secondary) #60K35 (primary) #FOS: Mathematics #Probability (math.PR) #math.PR #msc:05C80 #msc:60K35
paper · pdf · doi:10.48550/arxiv.1505.06069
11 pages
arxiv created 2015/05/22 · arxiv updated 2015/05/25
We show that a superposition of an ε-Bernoulli bond percolation and any everywhere percolating subgraph of \mathbb Zd, d≥ 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.