Mustapha Mourragui and Enza Orlandi
 Large deviations from a macroscopic scaling limit for particle 
systems with Kac interaction and random potential.
(661K, pdf)

ABSTRACT.  We consider a lattice gas in a periodic $d-$ dimensional lattice of width $\g^{-1}$, $\g>0$, interacting via a Kac's type interaction, with range $\frac 1\g $ and strength $\g^d$, and 
under the influence of a random potential given by independent, 
bounded, random variables with translational invariant distribution. The system evolves through a conservative dynamics, i.e. particles jump to nearest neighbor empty sites, with 
 rates satisfying detailed balance with respect to the equilibrium measures. In [MOS] it has been shown that rescaling space as 
$\g^{-1}$ and time as $\g^{-2}$, in the limit $\g \to 0$, for dimensions $d\ge 3$, the macroscopic density profile $\r$ satisfies, a.s. with respect to the random field, a nonlinear integral 
partial differential equation, having the diffusion matrix 
determined by the statistical properties of the external random field. Here we show an almost sure (with respect to the random 
field) large deviations principle for the empirical measures of such a process. The rate function, which depends on the 
statistical properties of the external random field, is 
 lower semicontinuous and has compact level sets.