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Analysis and Stochastics of Growth Processes and Interface Models$
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Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer

Print publication date: 2008

Print ISBN-13: 9780199239252

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199239252.001.0001

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Large Deviations for Empirical Cycle Counts of Integer Partitions and Their Relation to Systems of Bosons

Large Deviations for Empirical Cycle Counts of Integer Partitions and Their Relation to Systems of Bosons

Chapter:
(p.148) 7 Large Deviations for Empirical Cycle Counts of Integer Partitions and Their Relation to Systems of Bosons
Source:
Analysis and Stochastics of Growth Processes and Interface Models
Author(s):

Stefan Adams

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199239252.003.0007

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.

Keywords:   Bose gas, empirical shape measure, empirical path measure, interacting Brownian motion, large deviations technique, cycle structure, phase transition

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