Algebraic surprises of the infinite beta random matrix theory

Seminar: 
Colloquium
Event time: 
Wednesday, November 11, 2020 - 4:15pm
Speaker: 
Vadim Gorin
Speaker affiliation: 
University of Wisconsin - Madison
Event description: 

Abstract: 

Dyson’s threefold approach suggests to deal with real/complex/quaternion random matrices as beta=1/2/4 instances of beta-ensembles.

We complement this approach by the new beta=\infty point, whose study reveals a number of previously unnoticed algebraic structures.
Our central object is the G\inftyE ensemble, which is a counterpart of the classical Gaussian Orthogonal/Unitary/Symplectic ensembles. We encounter unusual orthogonal polynomials, random walks, and finite free polynomial convolutions.