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Critical point and percolation probability in a long range site percolation model on

Author

Listed:
  • de Lima, Bernardo N.B.
  • Sanchis, Rémy
  • Silva, Roger W.C.

Abstract

Consider an independent site percolation model with parameter p[set membership, variant](0,1) on , where there are only nearest neighbor bonds and long range bonds of length k parallel to each coordinate axis. We show that the percolation threshold of such a model converges to when k goes to infinity, the percolation threshold for ordinary (nearest neighbor) percolation on . We also generalize this result for models whose long range bonds have several lengths.

Suggested Citation

  • de Lima, Bernardo N.B. & Sanchis, Rémy & Silva, Roger W.C., 2011. "Critical point and percolation probability in a long range site percolation model on," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2043-2048, September.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:9:p:2043-2048
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