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On the truncated anisotropic long-range percolation on

Author

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

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.

Suggested Citation

  • Sidoravicius, V. & Surgailis, D. & Vares, M. E., 1999. "On the truncated anisotropic long-range percolation on," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 337-349, June.
    • Handle: RePEc:eee:spapps:v:81:y:1999:i:2:p:337-349
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    Cited by:

    1. Misumi, Jun, 2013. "Estimates on the effective resistance in anisotropic long-range percolation on Z2," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 953-959.

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