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Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram. (English) Zbl 1009.05134

Summary: The Schur process is a time-dependent analog of the Schur measure on partitions studied by A. Okounkov [Infinite wedge and random partitions, Sel. Math., New Ser. 7, 57-81 (2001; Zbl 0986.05102)]. 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.

MSC:

05E05 Symmetric functions and generalizations
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)

Citations:

Zbl 0986.05102
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References:

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