zbMATH — the first resource for mathematics

Homogenization via sprinkling. (English. French summary) Zbl 1370.60186
Summary: We show that a superposition of an \(\varepsilon\)-Bernoulli bond percolation and any everywhere percolating subgraph of \(\mathbb{Z}^{d}\), \(d\geq 2\), results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli percolation. This result, which confirms a conjecture from [the first author et al., J. Math. Phys. 41, No. 3, 1294–1297 (2000; Zbl 0977.82021)], is mainly motivated by obtaining finite volume characterizations of uniqueness for general percolation processes.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
05C80 Random graphs (graph-theoretic aspects)
Full Text: DOI Euclid arXiv