Quenched scaling limits of trap models
| dc.creator | Jara, M. | |
| dc.creator | Landim, C. | |
| dc.creator | Teixeira, A. | |
| dc.date | 2009-02-19 | |
| dc.date.accessioned | 2026-07-07T12:44:09Z | |
| dc.date.available | 2026-07-07T12:44:09Z | |
| dc.description | Fix a strictly positive measure $W$ on the $d$-dimensional torus $\bb T^d$. For an integer $N\ge 1$, denote by $W^N_x$, $x=(x_1, ..., x_d)$, $0\le x_i <N$, the $W$-measure of the cube $[x/N, (x+\mb 1)/N)$, where $\mb 1$ is the vector with all components equal to 1. In dimension 1, we prove that the hydrodynamic behavior of a superposition of independent random walks, in which a particle jumps from $x/N$ to one of its neighbors at rate $(N W^N_x)^{-1}$, is described in the diffusive scaling by the linear differential equation $\partial_t ρ= (d/dW)(d/dx) ρ$. In dimension $d>1$, if $W$ is a finite discrete measure, $W=\sum_{i\ge 1} w_i δ_{x_i}$, 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}. | |
| dc.identifier | https://arxiv.org/abs/0902.3334 | |
| dc.identifier | http://arxiv.org/abs/0902.3334 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220671 | |
| dc.subject | Probability | |
| dc.subject | 60K35 | |
| dc.title | Quenched scaling limits of trap models | |
| dc.type | text |