Homogenization via sprinkling
Itai Benjamini, Vincent Tassion
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Abstract
We show that a superposition of an -Bernoulli bond percolation and any everywhere percolating subgraph of , , 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 H\"aggstr\"om and Schramm (2000), is mainly motivated by obtaining finite volume characterizations of uniqueness for general percolation processes.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Markov Chains and Monte Carlo Methods