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Large deviations for empirical cycle counts of integer partitions and their relation to systems of Bosons

By S. (Stefan) Adams


Motivated by the Bose gas, this chapter introduces certain combinatorial structures. It analyses 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 that are analysed. A symmetrized system of Brownian motions is highly correlated and has to be formulated such that standard techniques can be applied. The chapter reviews a novel spatial and a novel cycle structure approach for the symmetrized distributions of the empirical path measures. The cycle structure leads to a proof of a phase transition in the mean path measure

Topics: QA
Publisher: Oxford University Press
Year: 2008
DOI identifier: 10.1093/acprof:oso/9780199239252.003.0007
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