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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.

MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 05C80 Random graphs (graph-theoretic aspects)
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