Show simple item record

Existence of a non-averaging regime for the self-avoiding walk on a high-dimensional infinite percolation cluster

dc.contributor.authorLacoin, Hubert
dc.date.accessioned2014-01-10T15:48:26Z
dc.date.available2014-01-10T15:48:26Z
dc.date.issued2014
dc.identifier.issn0022-4715
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12403
dc.language.isoenen
dc.subjectPercolation
dc.subjectDisorder relevance
dc.subjectSelf-avoiding walk
dc.subjectRandom media
dc.subjectPolymers
dc.subject.ddc520en
dc.titleExistence of a non-averaging regime for the self-avoiding walk on a high-dimensional infinite percolation cluster
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenLet Z_N be the number of self-avoiding paths of length N starting from the origin on the infinite cluster obtained after performing Bernoulli percolation on Z^d with parameter p>p_c(Z^d). The object of this paper is to study the connective constant of the dilute lattice \limsup_{N\to \infty} Z_N^{1/N}, which is a non-random quantity. We want to investigate if the inequality \limsup_{N\to \infty} (Z_N)^{1/N} \le \lim_{N\to \infty} E[Z_N]^{1/N} obtained with the Borel-Cantelli Lemma is strict or not. In other words, we want to know the the quenched and annealed versions of the connective constant are the same. On a heuristic level, this indicates whether or not localization of the trajectories occurs. We prove that when d is sufficiently large there exists p^{(2)}_c>p_c such that the inequality is strict for p\in (p_c,p^{(2)}_c).
dc.relation.isversionofjnlnameJournal of Statistical Physics
dc.relation.isversionofjnlvol154
dc.relation.isversionofjnlissue6
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages1461-1482
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s10955-014-0926-x
dc.relation.isversionofjnlpublisherKluwer Academic Publishers etc.
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2016-09-24T13:35:47Z


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record