Local moderate and precise large deviations via cluster expansions

Giuseppe Scola

Published 2020-01-16Version 1

We consider a system of classical particles confined in a box $\Lambda \subset \mathbb{R}^d$ with general boundary conditions interacting via a stable and regular pair potential. Based on the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime we prove moderate and precise large deviations from the mean value of the number of particles with respect to the grand-canonical Gibbs measure. In this way we have a direct method of computing both the exponential rate as well as the pre-factor and obtain explicit error terms. Estimates comparing with the infinite volume versions of the above are also provided.