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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.
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.
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