Matrix concentration inequalities via the method of exchangeable pairs

This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein’s method of exchangeable pairs. When applied to a sum of independent random matrices, this approach yields matrix gen-eralizations of the classical inequalities due to Hoeffding, Bernstein, Khint-chine and Rosenthal. The same technique delivers bounds for sums of depen-dent random matrices and more general matrix-valued functions of dependent random variables