Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
93/2007

About large deviations for empirical path measures of cycle counts of integer partitions and their relation to systems of Bosons

Stefan Adams

Abstract

Motivated by the Bose gas we introduce certain combinatorial structures. We analyse the asymptotic behaviour of empirical shape measures and of empirical path measures of $ N $ Brownian motions with large deviations techniques. The rate functions are given as variational problems which we analyse. A symmetrised system of Brownian motions, that is, for any $i$, the terminal location of the $i$-th motion is affixed to the initial point of the $\sigma(i)$-th motion, where $\sigma$ is a uniformly distributed random permutation of $1,\dots,N$, is highly correlated and has to be formulated such that standard techniques can be applied. We review a novel spatial and a novel cycle structure approach for the symmetrised distributions of the empirical path measures. The cycle structure leads to a proof of a phase transition in the mean path measure.

Received:
Sep 27, 2007
Published:
Sep 27, 2007
MSC Codes:
60F10, 60J65, 82B10, 82B26
Keywords:
large deviations, integer partitions, path measure, Brownian bridges, symmetrised distribution, combinatorial structures

Related publications

Preprint
2007 Repository Open Access
Stefan Adams

About large deviations for empirical path measures of cycle counts of integer partitions and their relation to systems of Bosons