Hydrodynamic limit of zero range processes among random conductances on the supercritical percolation cluster
Alessandra Faggionato, Department of Mathematics. University La Sapienza, Rome. Italy
Abstract
We consider i.i.d. random variables omega={omega(b)}
parameterized by the family of bonds in 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 Z^d with
conductance field omega. We do not require any ellipticity
condition.
Full text: PDF
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona. You can even send a scanned jpeg or pdf of this copyright form to the managing editor ejpecpme@math.univ-nantes.fr. as an attached file.
If a paper has several authors, the corresponding author signs the copyright form on behalf of all the authors.