Conference abstracts

Session B5 - Random Matrices

July 14, 15:00 ~ 15:25

Self-similarity in the spectra of random unitary matrices

Mark Meckes

Case Western Reserve University, USA   -   mark.meckes@case.edu

I will present a rigorous result roughly stating that, for a range of mesoscopic scales, the eigenvalues of an $n \times n$ random unitary matrix are statistically indistinguishable from those of a $2n \times 2n$ matrix, suitably rescaled. This result is inspired by a conjecture made by Coram and Diaconis in a statistical study of the relationship between eigenvalues of large random unitary matrices and zeroes of the Riemann zeta function.

Joint work with Elizabeth Meckes (Case Western Reserve University).

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FoCM 2017, based on a nodethirtythree design.