Percolation of Words on Zd with Long-Range Connections
2011 ◽
Vol 48
(4)
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pp. 1152-1162
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Keyword(s):
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.
Keyword(s):
2011 ◽
Vol 121
(9)
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pp. 2043-2048
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Keyword(s):
2009 ◽
Vol 17
(1)
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pp. 1-35
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1998 ◽
Vol 41
(2)
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pp. 166-177
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2004 ◽
Vol 159
(3)
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pp. 949-960
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Keyword(s):
2009 ◽
Vol 18
(1-2)
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pp. 83-106
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Keyword(s):
1980 ◽
Vol 38
(3)
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pp. 267-270
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