Permanental Partition Models and Markovian Gibbs Structures

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Abstract

We study both time-invariant and time-varying Gibbs distributions for configurations of particles into disjoint clusters. Specifically, we introduce and give some fundamental properties for a class of partition models, called permanental partition models, whose distributions are expressed in terms of the α-permanent of a similarity matrix parameter. We show that, in the time-invariant case, the permanental partition model is a refinement of the celebrated Pitman-Ewens distribution; whereas, in the time-varying case, the permanental model refines the Ewens cut-and-paste Markov chains (J. Appl. Probab. 43(3):778-791, 2011). By a special property of the α-permanent, the partition function can be computed exactly, allowing us to make several precise statements about this general model, including a characterization of exchangeable and consistent permanental models.

Original languageEnglish (US)
Pages (from-to)698-726
Number of pages29
JournalJournal of Statistical Physics
Volume153
Issue number4
DOIs
StatePublished - Nov 1 2013

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Boltzmann-Gibbs measure
  • Canonical Gibbs ensemble
  • Markovian Gibbs structure
  • Permanental partition model
  • Permanental process
  • α-Permanent

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