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November 2014 Universality of trap models in the ergodic time scale
M. Jara, C. Landim, A. Teixeira
Ann. Probab. 42(6): 2497-2557 (November 2014). DOI: 10.1214/13-AOP886

Abstract

Consider a sequence of possibly random graphs $G_{N}=(V_{N},E_{N})$, $N\ge1$, whose vertices’s have i.i.d. weights $\{W^{N}_{x}:x\in V_{N}\}$ with a distribution belonging to the basin of attraction of an $\alpha$-stable law, $0<\alpha<1$. Let $X^{N}_{t}$, $t\ge0$, be a continuous time simple random walk on $G_{N}$ which waits a mean $W^{N}_{x}$ 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, $d\ge2$, random $d$-regular graphs and the largest component of super-critical Erdős–Rényi random graphs.

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M. Jara. C. Landim. A. Teixeira. "Universality of trap models in the ergodic time scale." Ann. Probab. 42 (6) 2497 - 2557, November 2014. https://doi.org/10.1214/13-AOP886

Information

Published: November 2014
First available in Project Euclid: 30 September 2014

zbMATH: 1305.35044
MathSciNet: MR3265173
Digital Object Identifier: 10.1214/13-AOP886

Subjects:
Primary: 60J27 , 60K37 , 82C41

Keywords: metastability , Scaling limit , trap models

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 6 • November 2014
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