Infinite wedge and random partitions

Andrei Okounkov

Research output: Contribution to journalArticlepeer-review

159 Citations (Scopus)

Abstract

We use representation theory to obtain a number of exact results for random partitions. In particular, we prove a simple determinantal formula for correlation functions of what we call the Schur measure on partitions (which is a far reaching generalization of the Plancherel measure; see [3], [8]) and also observe that these correlations functions are τ-functions for the Toda lattice hierarchy. We also give a new proof of the formula due to Bloch and the author [5] for the so-called n-point functions of the uniform measure on partitions and comment on the local structure of a typical partition.

Original languageEnglish
Pages (from-to)57-81
Number of pages25
JournalSelecta Mathematica, New Series
Volume7
Issue number1
DOIs
Publication statusPublished - 2001
Externally publishedYes

Keywords

  • Random partitions
  • Schur measure

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