#### 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).