### Hydrodynamical limit for space inhomogeneous one-dimensional totally asymmetric zero-range processes

C. Landim
Source: Ann. Probab. Volume 24, Number 2 (1996), 599-638.

#### 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.

First Page:
Primary Subjects: 60K35, 82C22, 82C24
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.aop/1039639356
Mathematical Reviews number (MathSciNet): MR1404522
Digital Object Identifier: doi:10.1214/aop/1039639356
Zentralblatt MATH identifier: 0862.60095

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