Electronic Communications in Probability

On the spectral norm of a random Toeplitz matrix

Mark Meckes

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465224974

Digital Object Identifier
doi:10.1214/ECP.v12-1313

Mathematical Reviews number (MathSciNet)
MR2342710

Zentralblatt MATH identifier
1130.15018

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

Keywords
random Toeplitz matrix random Hankel matrix spectral norm

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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