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Interacting Brownian particles and Gibbs fields on pathspaces

Published online by Cambridge University Press:  15 May 2003

David Dereudre*
Affiliation:
Centre de Mathématiques Appliquées, UMR 7641, École Polytechnique, 91128 Palaiseau Cedex, France; dereudre@cmapx.polytechnique.fr.
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Abstract

In this paper, we prove that the laws of interacting Brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of Hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to Brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2003

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