Local moderate and precise large deviations via cluster expansions

Abstract

We consider a system of classical particles confined in a box $\Lambda \subset {\mathbb{R}}^d$ with zero 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.

arXiv comment26 pages

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• Abstract cluster expansion with applications to statistical mechanical systems
• Cluster expansion in the canonical ensemble
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Cited by in corpus (1)

• Cluster expansion for the Ising model in the canonical ensemble