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.
Back to Free Entropy Theory and Random Matrices
Copyright. All Rights Reserved.