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Poisson-Dirichlet asymptotics in condensing particle systems
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Chleboun, Paul, Gabriel, Simon and Grosskinsky, Stefan (2022) Poisson-Dirichlet asymptotics in condensing particle systems. Electronic Journal of Probability, 27 . doi:10.1214/22-ejp882 ISSN 1083-6489.
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Official URL: https://doi.org/10.1214/22-ejp882
Abstract
We study measures on random partitions, arising from condensing stochastic particle systems with stationary product distributions. We provide fairly general conditions on the stationary weights, which lead to Poisson-Dirichlet statistics of the condensed phase in the thermodynamic limit. The Poisson-Dirichlet distribution is known to be the unique reversible measure of split-merge dynamics for random partitions, which we use to characterize the limit law. We also establish concentration results for the macroscopic phase, using size-biased sampling techniques and the equivalence of ensembles to characterize the bulk distribution of the system.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
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SWORD Depositor: | Library Publications Router | ||||||
Library of Congress Subject Headings (LCSH): | Poisson distribution, Poisson processes, Mathematical statistics, Distribution (Probability theory), Partitions (Mathematics) | ||||||
Journal or Publication Title: | Electronic Journal of Probability | ||||||
Publisher: | University of Washington. Dept. of Mathematics | ||||||
ISSN: | 1083-6489 | ||||||
Official Date: | 1 December 2022 | ||||||
Dates: |
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Volume: | 27 | ||||||
Number of Pages: | 35 | ||||||
DOI: | 10.1214/22-ejp882 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 4 January 2023 | ||||||
Date of first compliant Open Access: | 4 January 2023 | ||||||
RIOXX Funder/Project Grant: |
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