Georgia Institute of Technology College of Sciences

Beta-ensembles generalize the eigenvalue distributions of self-adjoint
real, complex, and quaternion matrices for beta=1,2, and 4,
respectively. These ensembles naturally extend to two dimensions by
introducing operations such as corner truncation, addition, or
multiplication of matrices. In this talk, we will explore the edge
asymptotics of the resulting two-dimensional ensembles. I will present
the Airy-beta line ensemble, a universal object that governs the
asymptotics of time-evolving largest eigenvalues. This ensemble
consists of an infinite collection of continuous random curves,
parameterized by beta. I will share recent progress in developing a
framework to describe this remarkable structure.