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dc.contributor.authorLacoin, Hubert
dc.date.accessioned2013-09-04T14:28:21Z
dc.date.available2013-09-04T14:28:21Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/11608
dc.language.isoenen
dc.subjectpercolationen
dc.subjectgrowth modelen
dc.subjectdirected polymersen
dc.subjectphase transitionen
dc.subjectrandom mediaen
dc.subject.ddc519en
dc.titleExistence of an intermediate phase for oriented percolationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider the following oriented percolation model of N×Zd: we equip N×Zd with the edge set {[(n,x),(n+1,y)]|n∈N,x,y∈Zd}, and we say that each edge is open with probability pf(y−x) where f(y−x) is a fixed non-negative compactly supported function on Zd with ∑z∈Zdf(z)=1 and p∈[0,inff−1] is the percolation parameter. Let pc denote the percolation threshold ans ZN the number of open oriented-paths of length N starting from the origin, and study the growth of ZN when percolation occurs. We prove that for if d≥5 and the function f is sufficiently spread-out, then there exists a second threshold p(2)c>pc such that ZN/pN decays exponentially fast for p∈(pc,p(2)c) and does not so when p>p(2)c. The result should extend to the nearest neighbor-model for high-dimension, and for the spread-out model when d=3,4. It is known that this phenomenon does not occur in dimension 1 and 2.en
dc.relation.isversionofjnlnameElectronic Journal of Probability
dc.relation.isversionofjnlvol17en
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages41en
dc.relation.isversionofdoihttp://dx.doi.org/10.1214/EJP.v17-1761en
dc.identifier.urlsitehttp://dx.doi.org/10.1214/EJP.v17-1761en
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statisticsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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