Harmonic analysis on the infinite symmetric group and random matrices

Alexei Borodin

University of Pennsylvania

November 8,
refreshments at 3:45pm


The problem of decomposing certain natural representations of the infinite symmetric group into irreducibles gives rise to a remarkable 2-parameter family of probability distributions on the Young diagrams. This family includes the images of the uniform measures on (generalized) permutations under the Robinson-Schensted-Knuth correspondence. When the size of the Young diagrams goes to infinity, the distributions tend to a certain determinantal stochastic point process on the real line. This process is similar to those describing the spectra of random unitary and Hermitian matrices. It also provides a complete solution to the initial representation theoretic problem. This is a joint work with Grigori Olshanski.

Speaker's Contact Info: borodine(at-sign)math.upenn.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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