### Infinite beta random matrix theory

Probability Seminar

21st April 2021, 4:00 pm – 5:00 pm

online, online

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 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.

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