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

Bernardo N.B. de Lima, Rémy Sanchis and Roger W.C. Silva

Stochastic Processes and their Applications, 2011, vol. 121, issue 9, 2043-2048

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.

Keywords: Long; range; percolation; Percolation; threshold (search for similar items in EconPapers)
Date: 2011
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