Tail bounds on the spectral norm of sub-exponential random matrices

Abstract

Let [Formula: see text] be an [Formula: see text] symmetric random matrix with independent but non-identically distributed entries. The deviation inequalities of the spectral norm of [Formula: see text] with Gaussian entries have been obtained by using the standard concentration of Gaussian measure results. This paper establishes an upper tail bound of the spectral norm of [Formula: see text] with sub-exponential entries. Our method relies upon a crucial ingredient of a novel chaining argument that essentially involves both the particular structure of the sets used for the chaining and the distribution of coordinates of a point on the unit sphere.