Z-Measures on partitions, Robinson-Schensted-Knuth correspondence, and beta=2 random matrix ensembles

Abstract

We suggest an hierarchy of all the results known so far about the connection of the asymptotics of combinatorial or representation theoretic problems with ``beta=2 ensembles'' arising in the random matrix theory. We show that all such results are, essentially, degenerations of one general situation arising from so-called generalized regular representations of the infinite symmetric group.

AMSTeX, 19 pages

Cited by in corpus (14)

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• Distribution of the first particle in discrete orthogonal polynomial ensembles
• Duality of orthogonal polynomials on a finite set
• Representation theory and random point processes
• Non-intersecting Paths, Random Tilings and Random Matrices
• Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model
• Plancherel representations of $U(\infty )$ and correlated Gaussian Free Fields
• Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes
• Determinantal probability measures
• sl(2) Operators and Markov Processes on Branching Graphs
• Z-measures on partitions related to the infinite Gelfand pair $(S(2\infty ),H(\infty ))$
• Discrete gap probabilities and discrete Painleve equations
• Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter