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Estimates on the effective resistance in anisotropic long-range percolation on Z2

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  • Misumi, Jun

Abstract

We consider a long-range percolation on a vertex set of a two-dimensional square lattice, where the probabilities that horizontally long bonds exist may be different from the probabilities that vertically long bonds exist. We give some estimates on the effective resistance in such a model. The precise order of the effective resistance can be represented by using s, and r, which are the parameters determining the magnitude of the range in the horizontal and vertical directions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:953-959
    DOI: 10.1016/j.spl.2013.01.010
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    1. 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.
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