Elect. Comm. in Probab. 12 (2007), 315–325 ELECTRONIC COMMUNICATIONS in PROBABILITY ON THE SPECTRAL NORM OF A RANDOM TOEPLITZ MATRIX

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 1 Introduction an