Limit Shapes for Gibbs Ensembles of Partitions

Ibrahim Fatkullin; Valeriy Slastikov

doi:10.1007/s10955-018-2117-7

Limit Shapes for Gibbs Ensembles of Partitions

Ibrahim Fatkullin, Valeriy Slastikov

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1545-1563
Number of pages	19
Journal	Journal of Statistical Physics
Volume	172
Issue number	6
DOIs	https://doi.org/10.1007/s10955-018-2117-7
State	Published - Sep 1 2018

Keywords

Aggregation
Limit shapes
Partitions of integers
Zero range processes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-018-2117-7

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title = "Limit Shapes for Gibbs Ensembles of Partitions",

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 = "Aggregation, Limit shapes, Partitions of integers, Zero range processes",

author = "Ibrahim Fatkullin and Valeriy Slastikov",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Slastikov, Valeriy

N1 - Funding Information: 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. Publisher Copyright: © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2018/9/1

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N2 - 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.

AB - 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.

KW - Aggregation

KW - Limit shapes

KW - Partitions of integers

KW - Zero range processes

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

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Limit Shapes for Gibbs Ensembles of Partitions

Abstract

Keywords

ASJC Scopus subject areas

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