an:06270947
Zbl 1302.82071
Crane, Harry
Permanental partition models and Markovian Gibbs structures
EN
J. Stat. Phys. 153, No. 4, 698-726 (2013).
00326340
2013
j
82C22
Boltzmann-Gibbs measure; canonical Gibbs ensemble; Markovian Gibbs structure; permanental partition model; \(\alpha\)-permanent; permanental process
Summary: 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 \textit{permanental partition models}, whose distributions are expressed in terms of the \(\alpha\)-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 [\textit{H. Crane}, J. Appl. Probab. 48, No. 3, 778--791 (2011; Zbl 1235.60092)]. By a special property of the \(\alpha\)-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.
Reviewer (Berlin)
Zbl 1235.60092