Limit Shapes for Gibbs Ensembles of Partitions
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We explicitly compute limit shapes for several grand canonical Gibbs ensembles of partitions of integers. These ensembles appear in models of aggregation and are also related to invariant measures of zero range and coagulation-fragmentation processes. We show, that all possible limit shapes for these ensembles fall into several distinct classes determined by the asymptotics of the internal energies of aggregates.
KeywordsLimit shapes Partitions of integers Aggregation Zero range processes
The authors are grateful to the anonymous reviewers for valuable suggestions and references. Ibrahim Fatkullin acknowledges support by the NSF Grant DMS-1056471. Valeriy Slastikov acknowledges support by the Leverhulme Research Grant, RPG-2014-226.
- 15.Pitman, J.: Combinatorial Stochastic Processes. Lecture Notes in Mathematics. University of California, Berkeley, Berkeley (2006)Google Scholar
- 16.Schmidt, A., Vershik, A.: Limit measures that arise in the asymptotic theory of symmetric groups. I, II. Teor. Verojatn. i Prim 22, 72–88 (1977)Google Scholar
- 17.Shiryaev, A.N.: Probability. Graduate Texts in Mathematics, vol. 95. Springer, New York (1996)Google Scholar
- 21.Yakubovich, YuV: Asymptotics of random partitions of a set. Zap. Nauchnykh Semin. POMI 223, 227–250 (1995)Google Scholar