On the eigenvalues of Brownian motion on \mathbb{U}(n)

Abstract: Much recent work in the study of random matrices has focused on the non-asymptotic theory; that is, the study of random matrices of fixed, large size. I will discuss one such example: the eigenvalues of unitary Brownian motion. I will describe an approach which gives uniform quantitative almost-sure estimates over fixed time intervals of the distance between the random spectral measures of this parametrized family of random matrices and the corresponding measures in a deterministic parametrized family \{\nu_t\}_{t\ge 0} of large-n limiting measures. I will also discuss larger time scales. This is joint work with Tai Melcher.

analysis of PDEsmetric geometry

Audience: researchers in the topic

Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

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