Selecta Mathematica

, 7:57

Infinite wedge and random partitions

  • A. Okounkov

DOI: 10.1007/PL00001398

Cite this article as:
Okounkov, A. Sel. math., New ser. (2001) 7: 57. doi:10.1007/PL00001398


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 partitionsSchur measure

Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

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