Operator-norm Sudakov minoration for Gaussian chaos of order two
We prove that an operator-norm separated family of matrices satisfies $\mathbb{E}\sup_{A\in T} G^{T}AG'\geq ca\log |T|$, where G,G'are independent standard Gaussian vectors and a is the separation. The main information estimate concerns arbitrary separated coisometries: conditional entropy is bounded by a source-depend...