Homogenization via sprinkling

Itai Benjamini; Vincent Tassion

doi:10.1214/16-AIHP746

Homogenization via sprinkling

Itai Benjamini, Vincent Tassion

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We show that a superposition of an ϵ-Bernoulli bond percolation and any everywhere percolating subgraph of Zd , d ≥ 2, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli percolation. This result, which confirms a conjecture from (J. Math. Phys. 41 (2000) 1294-1297), is mainly motivated by obtaining finite volume characterizations of uniqueness for general percolation processes.

Original language	English
Pages (from-to)	997-1005
Number of pages	9
Journal	Annales De L Institut Henri Poincare-Probabilites Et Statistiques
Volume	53
Issue number	2
DOIs	https://doi.org/10.1214/16-AIHP746
State	Published - May 2017

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/16-AIHP746

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abstract = "We show that a superposition of an ϵ-Bernoulli bond percolation and any everywhere percolating subgraph of Zd , d ≥ 2, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli percolation. This result, which confirms a conjecture from (J. Math. Phys. 41 (2000) 1294-1297), is mainly motivated by obtaining finite volume characterizations of uniqueness for general percolation processes.",

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AB - We show that a superposition of an ϵ-Bernoulli bond percolation and any everywhere percolating subgraph of Zd , d ≥ 2, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli percolation. This result, which confirms a conjecture from (J. Math. Phys. 41 (2000) 1294-1297), is mainly motivated by obtaining finite volume characterizations of uniqueness for general percolation processes.

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Homogenization via sprinkling

Abstract

All Science Journal Classification (ASJC) codes

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