#### Conference abstracts

Session B5 - Random Matrices

July 14, 15:00 ~ 15:25

## Self-similarity in the spectra of random unitary matrices

### 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).

FoCM 2017, based on a nodethirtythree design.