Asymptotics of Plancherel-type random partitions

Alexei Borodin, Grigori Olshanski

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

We present a solution to a problem suggested by Philippe Biane: we prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set Z+ of nonnegative integers. This can be viewed as an edge limit transition. The limit process is determined by a correlation kernel on Z+ which is expressed through the Hermite polynomials, we call it the discrete Hermite kernel. The proof is based on a simple argument which derives convergence of correlation kernels from convergence of unbounded self-adjoint difference operators. Our approach can also be applied to a number of other probabilistic models. As an example, we discuss a bulk limit for one more Plancherel-type model of random partitions.

Original languageEnglish
Pages (from-to)40-60
Number of pages21
JournalJournal of Algebra
Volume313
Issue number1 SPEC. ISS.
DOIs
Publication statusPublished - 1 Jul 2007
Externally publishedYes

Keywords

  • Correlation kernel
  • Determinantal processes
  • Plancherel measure
  • Random partitions

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