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Infinite beta random matrix theory
Probability| Speaker: | Vadim Gorin, University of Wisconsin |
| Location: | zoom |
| Start time: | Wed, Jun 2 2021, 4:10PM |
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.