On the diffusion of eigenvectors of random matrices
schedule le lundi 08 avril 2019 de 17h00 à 18h00
Organisé par : GTT LPSM
Intervenant : Lucas Benigni (LPSM)
Lieu : Sophie Germain - Salle 1016
Sujet : On the diffusion of eigenvectors of random matrices
Due to the many applications of eigenvectors of large random matrices, in quantum mechanics or statistics for instance, their behavior has been broadly studied. In this talk, we analyze the diffusion of eigenvectors for mesoscopic random perturbations of diagonal matrices. We can show that the eigenvectors entries are asymptotically Gaussian with a specific variance, localizing them onto an explicit part of the spectrum. This is called, in the physics literature, the bad metal phase and is only conjectured or even debated for more complex models. By seeing this model as a dynamics on symmetric matrices, we can analyze the system of differential equations followed by eigenvector moments.