Harmonic analysis on the infinite symmetric group and random matrices
University of Pennsylvania
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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