Large deviations in random matrix theory and number theory
Monday, September 26, 2022 - 3:45pm
Abstract: There are many connections between the statistical properties of random unitary matrices and various number theoretic functions including the Riemann zeta function. In particular, central limit theorems exist for both characteristic polynomials of randomly drawn unitary matrices and the Riemann zeta function, giving information on ’typical values’. One might instead be interested in ‘atypical’ behaviour, including questions of extreme values. I will discuss recent work with Louis-Pierre Arguin concerning large deviations of the Riemann zeta function, which coincides with the associated theorem in random matrix theory.