  Suppose that $T_n$ 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 $T_n$ is of the order $\sqrt{n \log n}$. The same result holds for
random Hankel matrices as well as other variants of random Toeplitz matrices
which have been studied in the literature.
