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Comparison of Finite Volume Canonical and Grand Canonical Gibbs Measures: The Continuous Case
Authors:Nicoletta Cancrini  Christel Tremoulet
Affiliation:(1) Dipartimento di Matematica, Università di L"rsquo"Aquila and INFM Unità di Roma "ldquo"La Sapienza"rdquo", Italia;(2) Département de mathématiques, Université de Cergy-Pontoise, site Saint Martin, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise-Cedex, France
Abstract:We consider a continuous gas with finite range positive pair potential and we assume that the cluster expansion convergence condition holds. We prove a sharp bound on the difference between the finite volume grand canonical and canonical expectation of local observable. The bound is given in terms of the support of the observable, of its grand canonical variance and of the volume on which the system is confined.
Keywords:Continuous systems  Gibbs measures  equivalence of ensembles.
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