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

Journal of the American Mathematical Society - Tập 16 Số 3 - Trang 581-603
Andreĭ Okounkov1, Nicolai Reshetikhin1
1Department of Mathematics, University of California at Berkeley, Evans Hall #3840, Berkeley, California 94720-3840

Tóm tắt

The Schur process is a time-dependent analog of the Schur measure on partitions studied by A. Okounkov inInfinite 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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Journal of the American Mathematical Society

Tập 16 Số 3

581-603

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