Spectral normof randomlarge dimensional noncentral toeplitz and hankelmatrices

Suppose sn 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.