Point processes and distributions on Young diagrams


Grigori Olshanski

Institute for Information Transmission Problems
University of Pennsylvania

Northeastern University

Thursday, October 14, 1999


Talk at 4:30 p.m. in 509 Lake Hall

Tea at 4:00 p.m. in 544 Nightingale Hall

Abstract:   We use the simplest example to illustrate new problems and phenomena in noncommutative harmonic analysis which arise when irreducible representations depend on infinitely many continuous parameters. We start with a remarkable family of probability distributions on the (finite) set of Young diagrams with a given number of boxes. These distributions originated from a problem of harmonic analysis on the infinite symmetric group. When the number of boxes goes to infinity, our random Young diagrams turn into random point configurations on the real line, or point processes. These processes can be described by certain correlation kernels which are very similar to the kernels arising from random matrices.
     This is a joint work with Alexei Borodin (U. Penn). No special prerequisites are assumed: all necessary notions will be explained in the talk.

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.
There is free parking available for people coming to the colloquium at Northeastern's visitor parking. The entrance is from Columbus Avenue, right next to the parking garage.

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