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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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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of 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:	Date Event 2008 Published
Number of Pages:	336
Page Range:	pp. 148-172
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Related URLs:	Publisher

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