Vadim Gorin

Infinite beta random matrix theory

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.