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MiS Preprint

Interacting Brownian motions and the Gross-Pitaevskii formula

Stefan Adams and Wolfgang König


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.

MSC Codes:
60F10, 60J65, 82B10, 82B26
large deviations, Gross-Pitaevskii-formula, interacting brownian motions, Bosons

Related publications

2008 Repository Open Access
Stefan Adams and Wolfgang König

Interacting Brownian motions and the Gross-Pitaevskii formula

In: Analysis and stochastics of growth processes and interface models : selected papers based on the presentations at a regional meeting of the London Mathematical Society and a workshop on `Analysis and stochastics of growth processes', Bath, UK, September 11-15, 2006 / Peter Mörters (ed.)
Oxford : Oxford University Press, 2008. - pp. 173-193