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2011 Pfaffian Stochastic Dynamics of Strict Partitions
Leonid Petrov
Author Affiliations +
Electron. J. Probab. 16: 2246-2295 (2011). DOI: 10.1214/EJP.v16-956

Abstract

We study a family of continuous time Markov jump processes on strict partitions (partitions with distinct parts) preserving the distributions introduced by Borodin (1997) in connection with projective representations of the infinite symmetric group. The one-dimensional distributions of the processes (i.e., the Borodin's measures) have determinantal structure. We express the dynamical correlation functions of the processes in terms of certain Pfaffians and give explicit formulas for both the static and dynamical correlation kernels using the Gauss hypergeometric function. Moreover, we are able to express our correlation kernels (both static and dynamical) through those of the z-measures on partitions obtained previously by Borodin and Olshanski in a series of papers. The results about the fixed time case were announced in the note [El. Comm. Probab., 15 (2010), 162-175]. A part of the present paper contains proofs of those results.

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Leonid Petrov. "Pfaffian Stochastic Dynamics of Strict Partitions." Electron. J. Probab. 16 2246 - 2295, 2011. https://doi.org/10.1214/EJP.v16-956

Information

Accepted: 15 November 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1244.60083
MathSciNet: MR2861674
Digital Object Identifier: 10.1214/EJP.v16-956

Subjects:
Primary: 60G55
Secondary: 05E18, 60J75

JOURNAL ARTICLE
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Vol.16 • 2011
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