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.
Publié le : 1996-04-14
Classification:
Particle systems,
hydrodynamical behavior,
conservation laws,
large deviations,
60K35,
82C22,
82C24
@article{1039639356,
author = {Landim, C.},
title = {Hydrodynamical limit for space inhomogeneous one-dimensional
totally asymmetric zero-range processes},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 599-638},
language = {en},
url = {http://dml.mathdoc.fr/item/1039639356}
}
Landim, C. Hydrodynamical limit for space inhomogeneous one-dimensional
totally asymmetric zero-range processes. Ann. Probab., Tome 24 (1996) no. 2, pp. 599-638. http://gdmltest.u-ga.fr/item/1039639356/