We discuss recent results on the asymptotics of Hankel determinants with a multi-cut regular potential V. We will begin by considering an examples which is particularly simple (in particular V is given in terms of the Chebyshev polynomials), before continuing on to the general situation where the asymptotics are described in terms of Riemann's theta functions.

The motivation behind studying such determinants is to provide information about the asymptotic distribution of the eigenvalues of Hermitian random matrices with the potential V, and we will discuss the linear statistics of the eigenvalues under both smooth functions and jump functions.

The talk is based on joint work with Christophe Charlier, Christian Webb, and Mo Dick Wong. Speaker(s): Benjamin Fahs (KTH)