Benjamin Fahs: Toeplitz determinants, Hankel determinants, and random matrix theory

Abstract: We discuss the asymptotics of Toeplitz and Hankel determinants with Fisher-Hartwig singularities, and also those with symbols which are indicator functions. The motivation comes from the study of the statistics of unitary ensembles of random matrix theory, namely the statistics of the characteristic polynomials and gap probabilities of the eigenvalue distribution, respectively.