Benjamini, Itai; Tassion, Vincent Homogenization via sprinkling. (English. French summary) Zbl 1370.60186 Ann. Inst. Henri Poincaré, Probab. Stat. 53, No. 2, 997-1005 (2017). 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. Cited in 4 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 05C80 Random graphs (graph-theoretic aspects) Keywords:percolation; sprinkling; homogenization; finite-size criterion; random geometry Citations:Zbl 0977.82021 PDFBibTeX XMLCite \textit{I. Benjamini} and \textit{V. Tassion}, Ann. Inst. Henri Poincaré, Probab. Stat. 53, No. 2, 997--1005 (2017; Zbl 1370.60186) Full Text: DOI arXiv Euclid