Markov processes on partitions

Details Markov processes on partitions Markov processes on partitions

2004-09-29

arxiv.org/abs/math-ph/0409075v1

Probab. Theory Related Fields 135 (2006), no. 1, 84--152

Physics

Mathematical Physics

AMSTeX, 73 pages

Scientific paper

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.

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