C. Landim, HYDRODYNAMICAL LIMIT FOR SPACE INHOMOGENEOUS ONE-DIMENSIONAL TOTALLY ASYMMETRIC ZERO-RANGE PROCESSES, Annals of probability, 24(2), 1996, pp. 599-638
We consider totally asymmetric attractive zero-range processes with bo
unded 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 si
tes and slowdown the jump rate at these sites. We prove a hydrodynamic
al limit for this perturbed process and show the appearance of Dirac m
easures 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 l
imit is described by nonentropy weak solutions of quasilinear first-or
der hyperbolic equations. These two results prove that the large devia
tions for asymmetric processes with bounded jump rates are of order at
least e(-CN). All these results can be translated to the context of t
otally asymmetric simple exclusion processes where a finite number of
particles or a finite number of holes jump at a slower rate.