Percolation of words on $\Z^d$ with long range connections

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dc.creatorde Lima, Bernardo N. B.
dc.creatorSanchis, Remy
dc.creatorSilva, Roger W. C.
dc.date2009-05-28
dc.date.accessioned2026-07-07T13:18:48Z
dc.date.available2026-07-07T13:18:48Z
dc.descriptionConsider an independent site percolation model on $\Z^d$, with parameter $p \in (0,1)$, where all long range connections in the axes directions are allowed. In this work we show that given any parameter $p$, there exists and integer $K(p)$ such that all binary sequences (words) $ξ\in \{0,1\}^{\N}$ can be seen simultaneously, almost surely, even if all connections whose length is bigger than $K(p)$ are suppressed. We also show some results concerning the question how $K(p)$ should scale with $p$ when $p$ goes to zero. Related results are also obtained for the question of whether or not almost all words are seen.
dc.description10 pages, without figures
dc.identifierhttps://arxiv.org/abs/0905.4615
dc.identifierhttp://arxiv.org/abs/0905.4615
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/231546
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35, 82B41, 82B43
dc.titlePercolation of words on $\Z^d$ with long range connections
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