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Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
Author(s):
Andrei
Okounkov;
Nikolai
Reshetikhin
Journal:
J. Amer. Math. Soc.
16
(2003),
581-603.
MSC (2000):
Primary 05E05, 60G55
Posted:
March 3, 2003
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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
Email:
okounkov@math.berkeley.edu
Nikolai
Reshetikhin
Affiliation:
Department of Mathematics, University of California
at Berkeley, Evans Hall #3840, Berkeley, California
94720-3840
Email:
reshetik@math.berkeley.edu
DOI:
10.1090/S0894-0347-03-00425-9
PII:
S 0894-0347(03)00425-9
Received by editor(s):
December 8, 2001
Posted:
March 3, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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