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

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arxiv math/0107056 v3 pith:2J4HXP4C submitted 2001-07-06 math.CO math-phmath.MPmath.PRnlin.SI

classification math.COmath-phmath.MPmath.PRnlin.SI
keywords processschurdimensionalkernelrandomcorrelationdiagramfunction
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Schur process is a time-dependent analog of the Schur measure on partitions studied in math.RT/9907127. 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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Cited by 2 Pith papers

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  1. Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions

    math.PR 2025-07 conditional novelty 7.0 of 10

    For Aztec diamond tilings with i.i.d. one-periodic edge weights, height function fluctuations are, in the critical regime, GFF plus independent Brownian motion, and in the fixed-variance regime, Brownian motion alone ...

  2. A Two-Color Lift of the Shifted $t$-Schur Measure

    math.PR 2026-07 unverdicted novelty 6.0 of 10

    Introduces a two-color lift of the shifted Schur measure on pairs of partitions and derives its normalization, marginals, transition kernel, and independence of color volumes.

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