Electronic Communications in Probability

On the spectral norm of a random Toeplitz matrix

Mark Meckes

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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.

Article information

Electron. Commun. Probab., Volume 12 (2007), paper no. 31, 315-325.

Accepted: 3 October 2007
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15A52
Secondary: 60F99: None of the above, but in this section

random Toeplitz matrix random Hankel matrix spectral norm

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Meckes, Mark. On the spectral norm of a random Toeplitz matrix. Electron. Commun. Probab. 12 (2007), paper no. 31, 315--325. doi:10.1214/ECP.v12-1313. https://projecteuclid.org/euclid.ecp/1465224974

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