On the spectral norm of a random Toeplitz matrix

Details On the spectral norm of a random Toeplitz matrix On the spectral norm of a random Toeplitz matrix

2007-03-05

arxiv.org/abs/math/0703134v2

Electron. Commun. Probab. 12 (2007), 315-325

Mathematics

Probability

v2: Minor corrections and changes in exposition

Scientific paper

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.

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