Open Access
2010 Spectral norm of circulant type matrices with heavy tailed entries
Arup Bose, Rajat Hazra, Koushik Saha
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Electron. Commun. Probab. 15: 299-313 (2010). DOI: 10.1214/ECP.v15-1554


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.


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Arup Bose. Rajat Hazra. Koushik Saha. "Spectral norm of circulant type matrices with heavy tailed entries." Electron. Commun. Probab. 15 299 - 313, 2010.


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

zbMATH: 1226.60008
MathSciNet: MR2670197
Digital Object Identifier: 10.1214/ECP.v15-1554

Primary: 60B20
Secondary: 15A60 , 15B52 , 60B10 , 60F05

Keywords: Circulant matrix , Eigenvalues , Large dimensional random matrix , Moving average process , power transfer function , Reverse circulant matrix , spectral norm , symmetric circulant matrix , Toeplitz matrix

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