Limit Shapes for Gibbs Ensembles of Partitions

  title={Limit Shapes for Gibbs Ensembles of Partitions},
  author={Ibrahim Fatkullin and Valeriy V. Slastikov},
  journal={Journal of Statistical Physics},
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. 

Limit Shapes for Gibbs Partitions of Sets

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A Complete Bibliography of the Journal of Statistical Physics: 2000{2009

(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1



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  • J. Kingman
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1978
This characterization explains the robustness of the Ewens formula when neither selection nor recurrent mutation is significant, although different structures arise from selective and ‘charge-state’ models.

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