Spectral normof random large dimensional noncentral Toeplitz and Hankel matrices

Abstract

Suppose s_n is the spectral norm of either the Toeplitz or the Hankel matrix whose entries come from an i.i.d. sequence of random variables with positive mean μ and finite fourth moment. We show that n^-1/2(s_n-nμ) converges to the normal distribution in either case. This behaviour is in contrast to the known result for the Wigner matrices where s_n-nμ is itself asymptotically normal.