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Universality of trap models in the ergodic time scale

Jara, Milton; Landim, Claudio; Teixeira, Augusto (2014), Universality of trap models in the ergodic time scale, Annals of Probability, 42, 6, p. 2497-2557

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1208.5675v1
Date
2014
Journal name
Annals of Probability
Volume
42
Number
6
Publisher
IMS
Pages
2497-2557
Metadata
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Author(s)
Jara, Milton

Landim, Claudio

Teixeira, Augusto
Abstract (EN)
Consider a sequence of possibly random graphs GN=(VN,EN), N≥1, whose vertices's have i.i.d. weights {WNx:x∈VN} with a distribution belonging to the basin of attraction of an α-stable law, 0<α<1. Let XNt, t≥0, be a continuous time simple random walk on GN which waits a \emph{mean} WNx exponential time at each vertex x. Under considerably general hypotheses, we prove that in the ergodic time scale this trap model converges in an appropriate topology to a K-process. We apply this result to a class of graphs which includes the hypercube, the d-dimensional torus, d≥2, random d-regular graphs and the largest component of super-critical Erd\"os-R\'enyi random graphs.
Subjects / Keywords
trap model