Interacting Brownian motions and the Gross-Pitaevskii formula
Stefan Adams and Wolfgang König
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Submission date: 01. Sep. 2007
published 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 / P. Mörters (ed.)
Oxford : Oxford University Press, 2008. - P. 173 - 193
MSC-Numbers: 60F10, 60J65, 82B10, 82B26
Keywords and phrases: large deviations, Gross-Pitaevskii-formula, interacting brownian motions, Bosons
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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.