Infinite wedge and random partitions

• A. Okounkov ^[1]
  1. [1] University of California, USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 7, Nº. 1, 2001, págs. 57-81
• Idioma: inglés
• DOI: 10.1007/pl00001398
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• Resumen

  • 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.