Journal Title
Title of Journal: Probab Theory Relat Fields
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Abbravation: Probability Theory and Related Fields
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Publisher
Springer-Verlag
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Authors: Stefan Adams Wolfgang König
Publish Date: 2007/09/06
Volume: 142, Issue: 1-2, Pages: 79-124
Abstract
Consider a large system of N Brownian motions in mathbbRd with some nondegenerate initial measure on some fixed time interval 0β with symmetrised initialterminal condition That is for any i the terminal location of the ith motion is affixed to the initial point of the σith motion where σ is a uniformly distributed random permutation of 1N Such systems play an important role in quantum physics in the description of Boson systems at positive temperature 1/β In this paper we describe the largeN behaviour of the empirical path measure the mean of the Dirac measures in the N paths and of the mean of the normalised occupation measures of the N motions in terms of large deviations principles The rate functions are given as variational formulas involving certain entropies and Fenchel–Legendre transforms Consequences are drawn for asymptotic independence statements and laws of large numbers In the special case related to quantum physics our rate function for the occupation measures turns out to be equal to the wellknown Donsker–Varadhan rate function for the occupation measures of one motion in the limit of diverging time This enables us to prove a simple formula for the largeN asymptotic of the symmetrised trace of rm ebeta mathcalH N where mathcalH N is an Nparticle Hamilton operator in a trapThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team
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