 On the speed and spectrum of mean-field random walks among random conductancesAndrea Collevecchio and Paul Jung Stochastic Processes and their Applications, 2020, vol. 130, issue 6, 3477-3498 Abstract: We 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 Lévy 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→∞, 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. Keywords: Empirical spectral distribution; Speed; Rate of escape; Poisson weighted infinite tree; Random conductance model (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:6:p:3477-3498 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2019.10.001 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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