Strict inequality for bond percolation on a dilute lattice with columnar disorder

M.R. Hilário, M. Sá and R. Sanchis

Stochastic Processes and their Applications, 2022, vol. 149, issue C, 60-74

Abstract: We consider a dilute lattice obtained from the usual Z3 lattice by removing independently each of its columns with probability 1−ρ. In the remaining dilute lattice independent Bernoulli bond percolation with parameter p is performed. Let ρ↦pc(ρ) be the critical curve which divides the subcritical and supercritical phases. We study the behavior of this curve near the disconnection threshold ρc=pcsite(Z2) and prove that, uniformly over ρ it remains strictly below 1/2 (the critical point for bond percolation on the square lattice Z2).

Keywords: Percolation; Random media; Columnar disorder; Phase transition; Strict inequalities (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.03.003

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