Integrable Systems and Random Matrix Theory Seminar

In the first part of this talk, I will present recent results about large gap asymptotics on annuli in the random normal matrix model. In this two-dimensional setting, the theta function emerges in the asymptotics in a novel way which I will discuss (it is not related to Riemann-Hilbert problems).

In the second part of the talk, I will discuss about determinants with circular root- and jump-type singularities. These determinants are of interest in the study of the eigenvalue moduli of random normal matrices, but so far determinants with circular root-type singularities have been unexplored. I will show that such singular determinants have a novel type of asymptotic behavior described in terms of the so-called associated Hermite polynomials. Speaker(s): Christophe Charlier (Lund University)