# PDE & Analysis: Mark Ruselson (UMichigan) - No-gaps delocalization for general random matrices.

Title: No-gaps delocalization for general random matrices. Abstract: Heuristically, delocalization for a random matrix means that its normalized eigenvectors look like the vectors uniformly distributed over the unit sphere. This can be made precise in a number of different ways. We show that with high probability, any sufficiently large set of coordinates of an eigenvector carries a non-negligible portion of its Euclidean norm. Our results pertain to a large class of random matrices including matrices with independent entries, symmetric, skew-symmetric matrices, as well as more general ensembles. Joint work with Roman Vershynin.

## Date:

Thu, 31/03/2016 - 13:00 to 14:30

Ross 70