Markov processes on partitions

Abstract

We introduce and study a family of Markov processes on partitions. The processes preserve the so-called z-measures on partitions previously studied in connection with harmonic analysis on the infinite symmetric group. We show that the dynamical correlation functions of these processes have determinantal structure and we explicitly compute their correlation kernels. We also compute the scaling limits of the kernels in two different regimes. The limit kernels describe the asymptotic behavior of large rows and columns of the corresponding random Young diagrams, and the behavior of the Young diagrams near the diagonal. Our results show that recently discovered analogy between random partitions arising in representation theory and spectra of random matrices extends to the associated time-dependent models.

AMSTeX, 73 pages

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• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Discrete polynuclear growth and determinantal processes
• Eynard-Mehta theorem, Schur process, and their pfaffian analogs
• Differential Equations for Dyson Processes
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Cited by in corpus (6)

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• Pfaffian Stochastic Dynamics of Strict Partitions
• Random Strict Partitions and Determinantal Point Processes
• An interacting particle process related to Young tableaux
• Giambelli compatible point processes
• Markov dynamics on the Thoma cone: a model of time-dependent determinantal processes with infinitely many particles