Open Access
Translator Disclaimer
April 1996 Hydrodynamical limit for space inhomogeneous one-dimensional totally asymmetric zero-range processes
C. Landim
Ann. Probab. 24(2): 599-638 (April 1996). DOI: 10.1214/aop/1039639356

Abstract

We consider totally asymmetric attractive zero-range processes with bounded jump rates on Z. In order to obtain a lower bound for the large deviations from the hydrodynamical limit of the empirical measure, we perturb the process in two ways. We first choose a finite number of sites and slow down the jump rate at these sites. We prove a hydrodynamical limit for this perturbed process and show the appearance of Dirac measures on the sites where the rates are slowed down. The second type of perturbation consists of choosing a finite number of particles and making them jump at a slower rate. In these cases the hydrodynamical limit is described by nonentropy weak solutions of quasilinear first-order hyperbolic equations. These two results prove that the large deviations for asymmetric processes with bounded jump rates are of order at least $e^{-CN}$. All these results can be translated to the context of totally asymmetric simple exclusion processes where a finite number of particles or a finite number of holes jump at a slower rate.

Citation

Download Citation

C. Landim. "Hydrodynamical limit for space inhomogeneous one-dimensional totally asymmetric zero-range processes." Ann. Probab. 24 (2) 599 - 638, April 1996. https://doi.org/10.1214/aop/1039639356

Information

Published: April 1996
First available in Project Euclid: 11 December 2002

zbMATH: 0862.60095
MathSciNet: MR1404522
Digital Object Identifier: 10.1214/aop/1039639356

Subjects:
Primary: 60K35, 82C22, 82C24

Rights: Copyright © 1996 Institute of Mathematical Statistics

JOURNAL ARTICLE
40 PAGES


SHARE
Vol.24 • No. 2 • April 1996
Back to Top