Bernoulli line percolation

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 ∞.