On the spectral normof a randomtoeplitz matrix

Abstract

Suppose that Tn is a Toeplitz matrix whose entries come from a sequence of independent but not necessarily identically distributed random variables with mean zero. Under some additional tail conditions, we show that the spectral norm of Tn is of the order √n log n. The same result holds for random Hankel matrices as well as other variants of random Toeplitz matrices which have been studied in the literature © 2007 Applied Probability Trust.