Bernoulli line percolation

M.R. Hilário and V. Sidoravicius

Stochastic Processes and their Applications, 2019, vol. 129, issue 12, 5037-5072

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 ∞.

Date: 2019
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DOI: 10.1016/j.spa.2019.01.002

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