 05163 Mustapha Mourragui and Enza Orlandi
 Large deviations from a macroscopic scaling limit for particle
systems with Kac interaction and random potential.
(661K, pdf)
May 5, 05

Abstract ,
Paper (src),
View paper
(auto. generated pdf),
Index
of related papers

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.
 Files:
05163.src(
05163.keywords ,
R.pdf.mm )