Markov processes on partitions

Alexei Borodin, Grigori Olshanski

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)84-152
Number of pages69
JournalProbability Theory and Related Fields
Volume135
Issue number1
DOIs
Publication statusPublished - May 2006
Externally publishedYes

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