Poisson convergence of eigenvalues of circulant type matrices

Bose, Arup ; Hazra, Rajat Subhra ; Saha, Koushik (2011) Poisson convergence of eigenvalues of circulant type matrices Extremes, 14 (4). pp. 365-392. ISSN 1386-1999

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Official URL: http://doi.org/10.1007/s10687-010-0115-5

Related URL: http://dx.doi.org/10.1007/s10687-010-0115-5


We consider the point processes based on the eigenvalues of the reverse circulant, symmetric circulant and k-circulant matrices with i.i.d. entries and show that they converge to a Poisson random measures in vague topology. The joint convergence of upper ordered eigenvalues and their spacings follow from this. We extend these results partially to the situation where the entries are come from a two sided moving average process.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
Keywords:Circulant Matrix; K-Circulant Matrix; Eigenvalues; Large Dimensional Random Matrix; Moving Average Process; Normal Approximation; Point Process; Poisson Random Measure; Reverse Circulant Matrix; Spectral Density; Symmetric Circulant Matrix.
ID Code:121024
Deposited On:08 Jul 2021 10:47
Last Modified:08 Jul 2021 10:47

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