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Hydrodynamic Limit of Zero Range Processes Among Random Conductances on the Supercritical Percolation Cluster


 
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1. Title Title of document Hydrodynamic Limit of Zero Range Processes Among Random Conductances on the Supercritical Percolation Cluster
 
2. Creator Author's name, affiliation, country Alessandra Faggionato; University La Sapienza Rome; Italy
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) disordered system; bond percolation; zero range process; hydrodynamic limit; homogenization; stochastic domination
 
3. Subject Subject classification 60K35;60J27; 82C44
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2010-03-30
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/748
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-748
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
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