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Convergence rates for paths of the empirical spectral distribution of unitary Brownian motion

Banff International Research Station for Mathematical Innovation and Discovery

We will talk about convergence rates for the empirical spectral measure of a unitary Brownian motion. We give explicit bounds on the 1-Wasserstein distance of this measure to both the ensemble-averaged spectral measure and to the large-N limiting measure identified by Biane. We are then able to use these bounds to control the rate of convergence of paths of the measures on compact time intervals. The proofs use tools developed by the first author to study convergence rates of the classical random matrix ensembles, as well as recent estimates for the convergence of the moments of the ensemble-average spectral distribution.

Mathematics; Probability theory and stochastic processes; Partial differential equations

video/mp4

Author affiliation: University of Virginia

2019-03-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69069

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/