Limit Shapes for Gibbs Partitions of Sets

Ibrahim Fatkullin, Jianfei Xue

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - May 2021


  • Gibbs ensemble
  • Limit shape
  • Partition
  • Young diagram

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Limit Shapes for Gibbs Partitions of Sets'. Together they form a unique fingerprint.

Cite this