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- W4298291258 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 L'evy 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 goes to 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 that it has positive or weakly zero speed when the mean of the largest conductance is finite or infinite, respectively." @default.
- W4298291258 created "2022-10-01" @default.
- W4298291258 creator A5015245862 @default.
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- W4298291258 date "2017-02-14" @default.
- W4298291258 modified "2023-10-17" @default.
- W4298291258 title "On the speed and spectrum of mean-field random walks among random conductances" @default.
- W4298291258 doi "https://doi.org/10.48550/arxiv.1702.04087" @default.
- W4298291258 hasPublicationYear "2017" @default.
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