an:06729841
Zbl 1370.60186
Benjamini, Itai; Tassion, Vincent
Homogenization via sprinkling
EN
Ann. Inst. Henri Poincar??, Probab. Stat. 53, No. 2, 997-1005 (2017).
00366424
2017
j
60K35 05C80
percolation; sprinkling; homogenization; finite-size criterion; random geometry
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.
Zbl 0977.82021