Percolation of Words on Z d with Long-Range Connections
Keyword(s):
Consider an independent site percolation model onZd, with parameterp∈ (0, 1), where all long-range connections in the axis directions are allowed. In this work we show that, given any parameterp, there exists an integerK(p) such that all binary sequences (words) ξ ∈ {0, 1}Ncan be seen simultaneously, almost surely, even if all connections with length larger thanK(p) are suppressed. We also show some results concerning howK(p) should scale withpaspgoes to 0. Related results are also obtained for the question of whether or not almost all words are seen.
2011 ◽
Vol 48
(4)
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pp. 1152-1162
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2011 ◽
Vol 121
(9)
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pp. 2043-2048
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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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2009 ◽
Vol 18
(1-2)
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pp. 83-106
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1980 ◽
Vol 38
(3)
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pp. 267-270
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