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

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  • Hilário, M.R.
  • Sá, M.
  • Sanchis, R.

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).

Suggested Citation

  • Hilário, M.R. & Sá, M. & Sanchis, R., 2022. "Strict inequality for bond percolation on a dilute lattice with columnar disorder," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 60-74.
    • Handle: RePEc:eee:spapps:v:149:y:2022:i:c:p:60-74
    DOI: 10.1016/j.spa.2022.03.003
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    References listed on IDEAS

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    1. Hilário, M.R. & Sidoravicius, V., 2019. "Bernoulli line percolation," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5037-5072.
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