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Bernoulli line percolation

Author

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  • Hilário, M.R.
  • Sidoravicius, V.

Abstract

We study a percolation model on Zd, d≥3, in which the discrete lines of vertices parallel to the coordinate axes are entirely removed independently. We show the existence of a phase transition and establish that, for a certain range of the parameters including parts of both the subcritical and supercritical phases, the truncated connectivity function has power-law decay. For d=3, the power-law decay extends through all the supercritical phase. We also show that the number of infinite connected components is either 0, 1 or ∞.

Suggested Citation

  • Hilário, M.R. & Sidoravicius, V., 2019. "Bernoulli line percolation," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5037-5072.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:12:p:5037-5072
    DOI: 10.1016/j.spa.2019.01.002
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    Cited by:

    1. 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.

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