Infinite system of Brownian balls : equilibrium measures are canonical Gibbs

  • We consider a system of infinitely many hard balls in R<sup>d undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with a local time term. We prove that the set of all equilibrium measures, solution of a detailed balance equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.

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Author:Sylvie Roelly, Myriam Fradon
Document Type:Preprint
Date of Publication (online):2006/04/07
Year of Completion:2006
Publishing Institution:Universität Potsdam
Release Date:2006/04/07
Tag:Canonical Gibbs measure; Stochastic Differential Equation; detailed balance equation; hard core potential; reversible measure
Source:Stochastics and Dynamics. - 6 (2006), 1, S. 97 - 122
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Extern / Extern
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Collections:Universität Potsdam / Aufsätze (Pre- und Postprints) / Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik / Wahrscheinlichkeitstheorie
Notes extern:
AMS Classifications: 60H10 , 60J60 , 60K35

published at Stochastics and Dynamics. - 6 (2006), 1, S. 97 - 122
doi: 10.1142/S0219493706001669