Electronic Communications in Probability

Spectral norm of circulant type matrices with heavy tailed entries

Arup Bose, Rajat Hazra, and Koushik Saha

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Abstract

We first study the probabilistic properties of the spectral norm of scaled eigenvalues of large dimensional Toeplitz, circulant and symmetric circulant matrices when the input sequence is independent and identically distributed with appropriate heavy tails. When the input sequence is a stationary two sided moving average process of infinite order, we scale the eigenvalues by the spectral density at appropriate ordinates and study the limit for their maximums.

Article information

Source
Electron. Commun. Probab., Volume 15 (2010), paper no. 29, 299-313.

Dates
Accepted: 23 July 2010
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465243972

Digital Object Identifier
doi:10.1214/ECP.v15-1554

Mathematical Reviews number (MathSciNet)
MR2670197

Zentralblatt MATH identifier
1226.60008

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
Secondary: 15B52: Random matrices 60B10: Convergence of probability measures 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05] 60F05: Central limit and other weak theorems

Keywords
Large dimensional random matrix eigenvalues Toeplitz matrix circulant matrix symmetric circulant matrix reverse circulant matrix spectral norm moving average process power transfer function

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

Citation

Bose, Arup; Hazra, Rajat; Saha, Koushik. Spectral norm of circulant type matrices with heavy tailed entries. Electron. Commun. Probab. 15 (2010), paper no. 29, 299--313. doi:10.1214/ECP.v15-1554. https://projecteuclid.org/euclid.ecp/1465243972


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