Concentration of norms and eigenvalues of random matrices

Abstract

We prove concentration results for ${\ell }_p^n$ operator norms of rectangular random matrices and eigenvalues of self-adjoint random matrices. The random matrices we consider have bounded entries which are independent, up to a possible self-adjointness constraint. Our results are based on an isoperimetric inequality for product spaces due to Talagrand.

15 pages; AMS-LaTeX; updated one reference