Quenched scaling limits of trap models

Landim, Claudio; Jara, Milton; Quadros Teixeira, Augusto

Landim, Claudio; Jara, Milton; Quadros Teixeira, Augusto (2011), Quenched scaling limits of trap models, Annals of Probability, 39, 1, p. 176-223. http://dx.doi.org/10.1214/10-AOP554

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00362731/en/

Date

2011

Journal name

Annals of Probability

Volume

Number

Publisher

Institute of Mathematical Statistics

Pages

176-223

Abstract (EN)

Fix a strictly positive measure $W$ on the $d$-dimensional torus $\bb T^d$. For an integer $N\ge 1$, denote by $W^N_x$, $x=(x_1, \dots, x_d)$, $0\le x_i 1$, if $W$ is a finite discrete measure, $W=\sum_{i\ge 1} w_i \delta_{x_i}$, we prove that the random walk which jumps from $x/N$ uniformly to one of its neighbors at rate $(W^N_x)^{-1}$ has a metastable behavior, as defined in \cite{bl1}, described by the $K$-process introduced in \cite{fm1}.

Subjects / Keywords

hydrodynamique; Marches aléatoires; Environnement aléatoire