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2009 Limiting Spectral Distribution of Circulant Type Matrices with Dependent Inputs
Arup Bose, Rajat Hazra, Koushik Saha
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Electron. J. Probab. 14: 2463-2491 (2009). DOI: 10.1214/EJP.v14-714


Limiting spectral distribution (LSD) of scaled eigenvalues of circulant, symmetric circulant and a class of k-circulant matrices are known when the input sequence is independent and identically distributed with finite moments of suitable order. We derive the LSD of these matrices when the input sequence is a stationary, two sided moving average process of infinite order. The limits are suitable mixtures of normal, symmetric square root of the chisquare, and other mixture distributions, with the spectral density of the process involved in the mixtures.


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Arup Bose. Rajat Hazra. Koushik Saha. "Limiting Spectral Distribution of Circulant Type Matrices with Dependent Inputs." Electron. J. Probab. 14 2463 - 2491, 2009.


Accepted: 9 November 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1188.15033
MathSciNet: MR2563248
Digital Object Identifier: 10.1214/EJP.v14-714

Primary: 15A52
Secondary: 60F99 , 60G57 , 62E20

Keywords: $k$ circulant matrix , Circulant matrix , Eigenvalues , Empirical spectral distribution , Large dimensional random matrix , Limiting spectral distribution , Moving average process , norma , Reverse circulant matrix , Spectral density , symmetric circulant matrix

Vol.14 • 2009
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