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

Published online by Cambridge University Press:  01 March 2007

Myriam Fradon and
Sylvie Rœlly
Myriam Fradon
Affiliation:
Laboratoire CNRS 8524, UFR de Mathématiques, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France; Myriam.Fradon@univ-lille1.fr
Sylvie Rœlly
Affiliation:
Institut für Mathematik, Universität Potsdam, Am Neuen Palais, 14415 Potsdam, Germany; roelly@math.uni-potsdam.deOn leave of absence Centre de Mathématiques Appliquées, UMR CNRS 7641, École Polytechnique, 91128 Palaiseau Cedex, France.
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Abstract

We consider an infinite system of hard balls in $\xR^d$ undergoing Brownian motionsand submitted to a smooth pair potential.It is modelized by an infinite-dimensional stochastic differential equationwith 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 showthat Gibbs measures are reversible measures.

Keywords

Stochastic differential equationlocal timehard core potentialGibbs measurereversible measure.

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References

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