On a gateway between the Laguerre process and dynamics on partitions

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Abstract

Probability measures and stochastic dynamics on matrices and on partitions are related by standard, albeit technical, discrete to continuous scaling limits. In this paper we provide exact relations, that go in both directions, between the eigenvalues of the Laguerre process and certain distinguished dynamics on partitions. This is done by generalizing to the multidimensional setting recent results of Miclo and Patie on linear one-dimensional diffusions and birth and death chains. As a corollary, we obtain an exact relation between the Laguerre and Meixner ensembles. Finally, we explain the deep connections with the Young bouquet and the z-measures on partitions.
Original languageEnglish
Pages (from-to)1055–1076
Number of pages22
JournalLatin American Journal of Probability and Mathematical Statistics - ALEA
Volume16
DOIs
Publication statusPublished - 27 Sep 2019

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