Electronic Journal of Probability

Pfaffian Stochastic Dynamics of Strict Partitions

Leonid Petrov

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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.

Article information

Electron. J. Probab. Volume 16 (2011), paper no. 82, 2246-2295.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes
Secondary: 60J75: Jump processes 05E18: Group actions on combinatorial structures

random strict partitions determinantal point process Pfaffian dynamics

This work is licensed under a Creative Commons Attribution 3.0 License.


Petrov, Leonid. Pfaffian Stochastic Dynamics of Strict Partitions. Electron. J. Probab. 16 (2011), paper no. 82, 2246--2295. doi:10.1214/EJP.v16-956. https://projecteuclid.org/euclid.ejp/1464820251.

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