Please Note: This seminar will be given online.
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Department Seminar Benjamin Landon Link to join seminar: Hosted on Webex. |
Local eigenvalue statistics of random matrices and Dyson Brownian motion
Dyson Brownian motion is a stochastic process describing eigenvalue dynamics under a matrix-valued Brownian motion. This process has played a crucial role in the study of universality of the local spectral statistics of random matrices. We discuss results on the local ergodicity of Dyson Brownian motion and applications, including local eigenvalue universality of the adjacency matrices of sparse random graphs and an additive model related to free probability. We also review results on the universality of extremal spectral statistics and the fluctuations of a single eigenvalue in the spectral bulk. Finally, we discuss some systems of diffusions related to the KPZ universality class