Limit Shapes for Gibbs Partitions of Sets

Ibrahim Fatkullin, Jianfei Xue

Research output: Contribution to journalArticlepeer-review

Abstract

This study extends a prior investigation of limit shapes for grand canonical Gibbs ensembles of partitions of integers, which was based on analysis of sums of geometric random variables. Here we compute limit shapes for partitions of sets, which lead to the sums of Poisson random variables. Under mild monotonicity assumptions on the energy function, we derive all possible limit shapes arising from different asymptotic behaviors of the energy, and also compute local limit shape profiles for cases in which the limit shape is a step function.

Original languageEnglish (US)
Article number22
JournalJournal of Statistical Physics
Volume183
Issue number2
DOIs
StatePublished - May 2021

Keywords

  • Gibbs ensemble
  • Limit shape
  • Partition
  • Young diagram

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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