Abstract
Consider an independent site percolation model on Zd, with parameter p ∈ (0, 1), where all long-range connections in the axis directions are allowed. In this work we show that, given any parameter p, there exists an integer K(p) such that all binary sequences (words) ξ ∈ {0, 1}N can be seen simultaneously, almost surely, even if all connections with length larger than K(p) are suppressed. We also show some results concerning how K(p) should scale with p as p goes to 0. Related results are also obtained for the question of whether or not almost all words are seen.
Citation
B. N. B. de Lima. R. Sanchis. R. W. C. Silva. "Percolation of words on Zd with long-range connections." J. Appl. Probab. 48 (4) 1152 - 1162, December 2011. https://doi.org/10.1239/jap/1324046024
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