On the spectral norm of a random Toeplitz matrix

Abstract

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.

v2: Minor corrections and changes in exposition

References in corpus (2)

• Spectral measure of large random Hankel, Markov and Toeplitz matrices
• Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices