Electronic Journal of Probability

Limiting Spectral Distribution of Circulant Type Matrices with Dependent Inputs

Arup Bose, Rajat Hazra, and Koushik Saha

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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.

Article information

Electron. J. Probab., Volume 14 (2009), paper no. 86, 2463-2491.

Accepted: 9 November 2009
First available in Project Euclid: 1 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 62E20: Asymptotic distribution theory 60G57: Random measures

Large dimensional random matrix eigenvalues circulant matrix symmetric circulant matrix reverse circulant matrix $k$ circulant matrix empirical spectral distribution limiting spectral distribution moving average process spectral density norma

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Bose, Arup; Hazra, Rajat; Saha, Koushik. Limiting Spectral Distribution of Circulant Type Matrices with Dependent Inputs. Electron. J. Probab. 14 (2009), paper no. 86, 2463--2491. doi:10.1214/EJP.v14-714. https://projecteuclid.org/euclid.ejp/1464819547

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