|Date||Apr 20, 2017|
In this talk, I will introduce the distribution of eigenvalues of random normal matrix ensembles. Under the influence of an external potential, the eigenvalues tend to accumulate on a compact set and follow the equilibrium distribution. I will discuss the existence and universality of the microscopic densities of eigenvalues near a bulk singularity, an isolated point in the interior at which the equilibrium density vanishes. I will describe how the ward’s identity can be used to prove the universality and how we get the asymptotics for the Bergman function of some Fock-Sobolev spaces. This is joint work with Yacin Ameur.