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Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram

Authors: Andrei Okounkov and Nikolai Reshetikhin
Journal: J. Amer. Math. Soc. 16 (2003), 581-603
MSC (2000): Primary 05E05, 60G55
Published electronically: March 3, 2003
MathSciNet review: 1969205
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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

Nikolai Reshetikhin
Affiliation: Department of Mathematics, University of California at Berkeley, Evans Hall #3840, Berkeley, California 94720-3840

Received by editor(s): December 8, 2001
Published electronically: March 3, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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