## 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
- J. Amer. Math. Soc.
**16**(2003), 581-603 - DOI: https://doi.org/10.1090/S0894-0347-03-00425-9
- Published electronically: 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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## Bibliographic 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