The Annals of Probability

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

C. Landim

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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.

Article information

Ann. Probab., Volume 24, Number 2 (1996), 599-638.

First available in Project Euclid: 11 December 2002

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35] 82C24: Interface problems; diffusion-limited aggregation

Particle systems hydrodynamical behavior conservation laws large deviations


Landim, C. Hydrodynamical limit for space inhomogeneous one-dimensional totally asymmetric zero-range processes. Ann. Probab. 24 (1996), no. 2, 599--638. doi:10.1214/aop/1039639356.

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