Large deviations for the occupation times of independent particle systems

Abstract

prove a large deviation principle for the density field of independent particle systems in an infinite volume. We then deduce from the one-dimensional case of this result the large deviations for the occupation times of various sets (from microscopic to macroscopic scales) and we recover the theorem established by Cox and Griffeath. An expression of the rate function is given using the Brownian motion local time as in Deuschel and Wang.