Asymptotic analysis of the characteristic polynomial for the Elliptic Ginibre Ensemble.

The purpose of this talk is to show the convergence of the characteristic polynomial of random matrices sampled from the Elliptic Ginibre Ensemble, a model that interpolates between Ginibre and Gaussian Unitary Ensembles. The proof consists in two main steps: a control on the second moment using asymptotics of Hermite polynomials and the study of the fluctuations of traces using combinatorial arguments. We will expose each part of the proof together with future perspectives for the continuation of this work.