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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
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by Andrei Okounkov and Nikolai Reshetikhin PDF
J. Amer. Math. Soc. 16 (2003), 581-603 Request permission

Abstract:

The Schur process is a time-dependent analog of the Schur measure on partitions studied by A. Okounkov in Infinite wedge and random partitions, Selecta Math., New Ser. 7 (2001), 57–81. Our first result is that the correlation functions of the Schur process are determinants with a kernel that has a nice contour integral representation in terms of the parameters of the process. This general result is then applied to a particular specialization of the Schur process, namely to random 3-dimensional Young diagrams. The local geometry of a large random 3-dimensional diagram is described in terms of a determinantal point process on a 2-dimensional lattice with the incomplete beta function kernel (which generalizes the discrete sine kernel). A brief discussion of the universality of this answer concludes the paper.
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Additional Information
  • Andrei Okounkov
  • Affiliation: Department of Mathematics, University of California at Berkeley, Evans Hall #3840, Berkeley, California 94720-3840
  • MR Author ID: 351622
  • ORCID: 0000-0001-8956-1792
  • Email: okounkov@math.berkeley.edu
  • Nikolai Reshetikhin
  • Affiliation: Department of Mathematics, University of California at Berkeley, Evans Hall #3840, Berkeley, California 94720-3840
  • MR Author ID: 147195
  • Email: reshetik@math.berkeley.edu
  • Received by editor(s): December 8, 2001
  • Published electronically: March 3, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 16 (2003), 581-603
  • MSC (2000): Primary 05E05, 60G55
  • DOI: https://doi.org/10.1090/S0894-0347-03-00425-9
  • MathSciNet review: 1969205