On the generalization of the Wigner semicircle law to real symmetric tensors

par Razvan Gurau

jeudi 11 mars 2021, 14:00 → 15:00 Europe/Paris

A préciser

In this talk I will discuss a simple generalization of the resolvent to real symmetric tensors which yields a spectral representation of a subclass of tensor invariants. I will then discuss the expected resolvent for a random tensor distributed on a Gaussian (generalizing the Gaussian Orthogonal Ensemble) and show that the spectral density (discontinuity of the resolvent at the cut) respects a universal lay generalizing the Wigner semicircle law to higher order tensors. Finally I will discuss an application of this resolvent to the spiked tensor model.