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.
Funding Statement
S. Gabriel acknowledges financial support from EPSRC through grant EP/R513374/1.
Acknowledgments
S. Grosskinsky is grateful to Technical University of Delft, where part of this research was carried out. The authors thank the anonymous referees for valuable comments.
Citation
Paul Chleboun. Simon Gabriel. Stefan Grosskinsky. "Poisson-Dirichlet asymptotics in condensing particle systems." Electron. J. Probab. 27 1 - 35, 2022. https://doi.org/10.1214/22-EJP882
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