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Limit Shapes for Gibbs Ensembles of Partitions

  • Ibrahim Fatkullin
  • Valeriy Slastikov
Article
  • 20 Downloads

Abstract

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.

Keywords

Limit shapes Partitions of integers Aggregation Zero range processes 

Notes

Acknowledgements

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.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA
  2. 2.School of MathematicsUniversity of BristolBristolUK

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