ESAIM: P&S, February 2007, Vol. 11, pp. 55-79
DOI: 10.1051/ps:2007006

Infinite system of Brownian balls with interaction: the non-reversible case

Myriam Fradon¹ and Sylvie Roelly<sup>2, 3

1</sup>  Laboratoire CNRS 8524, UFR de Mathématiques, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France; Myriam.Fradon@univ-lille1.fr
²  Institut für Mathematik, Universität Potsdam, Am Neuen Palais, 14415 Potsdam, Germany; roelly@math.uni-potsdam.de
³  On leave of absence Centre de Mathématiques Appliquées, UMR CNRS 7641, École Polytechnique, 91128 Palaiseau Cedex, France.

(Invited paper accepted September 2005. Published online 1 March 2007.)

Abstract
We consider an infinite system of hard balls in undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.

Mathematics Subject Classification. 60H10, 60K35.

Key words: Stochastic differential equation, local time, hard core potential, Gibbs measure, reversible measure.


© EDP Sciences, SMAI 2007