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Stability of gas measures under perturbations and discretizations

Roberto Fernández

Department of Mathematics, Utrecht University, The Netherlands

E-mail Address: R.Fernandez1@uu.nl

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Pablo Groisman

IMAS-CONICET and Departamento de Matemática, FCEN-UBA, Argentina

NYU-ECNU, Institute of Mathematical Sciences, NYU Shanghai, P. R. China

E-mail Address: pgroisma@dm.uba.ar

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Santiago Saglietti

IMAS-CONICET and Departamento de Matemática, FCEN-UBA, Argentina

Departamento de Matemática, Pontificia Universidad Católica, Chile

E-mail Address: ssaglie@dm.uba.ar

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https://doi.org/10.1142/S0129055X16500227Cited by:3 (Source: Crossref)

Abstract

For a general class of gas models — which includes discrete and continuous Gibbsian models as well as contour or polymer ensembles — we determine a diluteness condition that implies: (1) uniqueness of the infinite-volume equilibrium measure; (2) stability of this measure under perturbations of parameters and discretization schemes, and (3) existence of a coupled perfect-simulation scheme for the infinite-volume measure together with its perturbations and discretizations. Some of these results have previously been obtained through methods based on cluster expansions. In contrast, our treatment is purely probabilistic and its diluteness condition is weaker than existing convergence conditions for cluster expansions.

Keywords:

AMSC: 60K35, 60G55, 82B31, 60J25, 65C35

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