On the speed and spectrum of mean-field random walks among random conductances

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dc.contributor.authorCollevecchio, Andreako
dc.contributor.authorJung, Paulko
dc.date.accessioned2020-05-19T01:20:05Z-
dc.date.available2020-05-19T01:20:05Z-
dc.date.created2020-01-03-
dc.date.created2020-01-03-
dc.date.issued2020-06-
dc.identifier.citationSTOCHASTIC PROCESSES AND THEIR APPLICATIONS, v.130, no.6, pp.3477 - 3498-
dc.identifier.issn0304-4149-
dc.identifier.urihttp://hdl.handle.net/10203/274230-
dc.description.abstractWe study random walk among random conductance (RWRC) on complete graphs with n vertices. The conductances are i.i.d. and the sum of conductances emanating from a single vertex asymptotically has an infinitely divisible distribution corresponding to a Levy subordinator with infinite mass at 0. We show that, under suitable conditions, the empirical spectral distribution of the random transition matrix associated to the RWRC converges weakly, as n -> infinity, to a symmetric deterministic measure on [-1, 1], in probability with respect to the randomness of the conductances. In short time scales, the limiting underlying graph of the RWRC is a Poisson Weighted Infinite Tree, and we analyze the RWRC on this limiting tree. In particular, we show that the transient RWRC exhibits a phase transition in which it has positive or weakly zero speed when the mean of the largest conductance is finite or infinite, respectively.-
dc.languageEnglish-
dc.publisherELSEVIER-
dc.titleOn the speed and spectrum of mean-field random walks among random conductances-
dc.typeArticle-
dc.identifier.wosid000530068500009-
dc.identifier.scopusid2-s2.0-85073998346-
dc.type.rimsART-
dc.citation.volume130-
dc.citation.issue6-
dc.citation.beginningpage3477-
dc.citation.endingpage3498-
dc.citation.publicationnameSTOCHASTIC PROCESSES AND THEIR APPLICATIONS-
dc.identifier.doi10.1016/j.spa.2019.10.001-
dc.contributor.localauthorJung, Paul-
dc.contributor.nonIdAuthorCollevecchio, Andrea-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorEmpirical spectral distribution-
dc.subject.keywordAuthorSpeed-
dc.subject.keywordAuthorRate of escape-
dc.subject.keywordAuthorPoisson weighted infinite tree-
dc.subject.keywordAuthorRandom conductance model-
dc.subject.keywordPlusGALTON-WATSON TREES-
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