| Título: | Hydrodynamic Limit of Zero Range Processes Among Random Conductances on the Supercritical Percolation Cluster |
| Autores: | Faggionato, Alessandra; University La Sapienza Rome |
| Fecha: | 2010-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
disordered system; bond percolation; zero range process; hydrodynamic limit; homogenization; stochastic domination 60K35;60J27; 82C44 |
| Descripción: | We consider i.i.d. random variables $\omega=\{\omega(b)\}$ parameterized by the family of bonds in $\mathbb{Z}^d$, $d > 1$. The random variable $\omega(b)$ is thought of as the conductance of bond $b$ and it ranges in a finite interval $[0,c_0]$. Assuming the probability of the event $\{\omega(b) > 0\}$ to be supercritical and denoting by $C(\omega)$ the unique infinite cluster associated to the bonds with positive conductance, we study the zero range process on $C(\omega)$ with $\omega(b)$-proportional probability rate of jumps along bond $b$. For almost all realizations of the environment we prove that the hydrodynamic behavior of the zero range process is governed by a nonlinear heat equation, independent from $\omega$. As byproduct of the above result and the blocking effect of the finite clusters, we discuss the bulk behavior of the zero range process on $\mathbb{Z}^d$ with conductance field $\omega$. We do not require any ellipticity condition. |
| Idioma: | No aplica |
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