Selecta Mathematica

, 7:57

Infinite wedge and random partitions

  • A. Okounkov


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 \( \tau \)-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.


Random partitions Schur measure 

Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  • A. Okounkov
    • 1
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

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