On the truncated anisotropic long-range percolation on

V. Sidoravicius, D. Surgailis and M. E. Vares

Stochastic Processes and their Applications, 1999, vol. 81, issue 2, 337-349

Abstract: Consider the following bond percolation process on : each vertex is connected to each of its nearest neighbour in the vertical direction with probability pv=[var epsilon]>0; and in the horizontal direction each vertex is connected to each of the vertices x±(i,0) with probability pi[greater-or-equal, slanted]0, i[greater-or-equal, slanted]1, with all different connections being independent. We prove that if pi's satisfy some regularity property, namely if pi[greater-or-equal, slanted]1/i ln i, for i sufficiently large, then for each [var epsilon]>0 there exists K[reverse not equivalent]K([var epsilon]) such that for truncated percolation process (for which if i[less-than-or-equals, slant]K and if j>K) the probability of the open cluster of the origin to be infinite remains positive.

Keywords: Long-range; percolation; Renormalization; Critical; probability (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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