2001/07/06 by Andrei Okounkov, Andreĭ Okounkov, Okounkov, Andrei +2 · 6 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.CO #math.MP #math.PR #nlin.SI
paper · pdf · doi:10.48550/arxiv.math/0107056
35 pages, 7 figures, to appear in JAMS
openalex publication_date 2001/07/06 · arxiv created 2003/01/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.