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Large deviations for empirical cycle counts of integer partitions and their relation to systems of Bosons
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Adams, S. (Stefan) (2008) Large deviations for empirical cycle counts of integer partitions and their relation to systems of Bosons. In: Mörters, Peter and Moser, Roger and Penrose, Mathew and Schwetlick, Hartmut and Zimmer, Johannes, (eds.) Analysis and stochastics of growth processes and interface models. Oxford: Oxford University Press, pp. 148-172. ISBN 9780199239252
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Official URL: http://webcat.warwick.ac.uk/record=b2253298~S1
Abstract
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.
Item Type: | Book Item | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Publisher: | Oxford University Press | ||||
Place of Publication: | Oxford | ||||
ISBN: | 9780199239252 | ||||
Book Title: | Analysis and stochastics of growth processes and interface models | ||||
Editor: | Mörters, Peter and Moser, Roger and Penrose, Mathew and Schwetlick, Hartmut and Zimmer, Johannes | ||||
Official Date: | 2008 | ||||
Dates: |
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Number of Pages: | 336 | ||||
Page Range: | pp. 148-172 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
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