Random partitions and the gamma kernel

Alexei Borodin, Grigori Olshanski

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young diagram and in the intermediate zone between the diagonal and the edge of the Young diagram. We prove that in both cases the limit correlation functions have determinantal form with a correlation kernel which depends on two real parameters. In the first case the correlation kernel is discrete, and it has a simple expression in terms of the gamma functions. In the second case the correlation kernel is continuous and translationally invariant, and it can be written as a ratio of two suitably scaled hyperbolic sines.

Original languageEnglish
Pages (from-to)141-202
Number of pages62
JournalAdvances in Mathematics
Issue number1
Publication statusPublished - 20 Jun 2005
Externally publishedYes


  • Determinantal point processes
  • Discrete orthogonal polynomials
  • Random partitions


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