Emma Bailey

Interpolation statistics for unlikely values of unitary characteristic polynomials

The logarithm of unitary characteristic polynomials is a Gaussian random variable when one draws the matrix under Haar measure. Large deviation principles and some precise deviations for this random variable are known following work of Hughes-Keating-O’Connell and Féray-Méliot-Nikeghbali. Motivated by a conjecture regarding the leading coefficient of the moments of the Riemann zeta function, we study a particular ‘interpolating regime’ in the right-tail. This is joint work with Sebastian Ortiz.