Stefan Adams, Wolfgang König
Published 2007-09-18Version 1
We review probabilistic approaches to the Gross-Pitaevskii theory describing interacting dilute systems of particles. The main achievement are large deviations principles for the mean occupation measure of a large system of interacting Brownian motions in a trapping potential. The corresponding rate functions are given as variational problems whose solution provide effective descriptions of the infinite system.
Large deviations for flows of interacting Brownian motions
Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials
Infinite-dimensional stochastic differential equations and tail $ σ$-fields
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