The spectral norm of Gaussian matrices with correlated entries

Afonso S. Bandeira, March T. Boedihardjo

Published 2021-04-06Version 1

We give a non-asymptotic bound on the spectral norm of a $d\times d$ matrix $X$ with centered jointly Gaussian entries in terms of the covariance matrix of the entries. In some cases, this estimate is sharp and removes the $\sqrt{\log d}$ factor in the noncommutative Khintchine inequality.