Abstract
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.
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Research of A. Bose supported by J. C. Bose National Fellowship, Dept. of Science and Technology, Govt. of India.
Research of K. Saha supported by CSIR Fellowship, Govt. of India.
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Bose, A., Hazra, R.S. & Saha, K. Poisson convergence of eigenvalues of circulant type matrices. Extremes 14, 365–392 (2011). https://doi.org/10.1007/s10687-010-0115-5
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DOI: https://doi.org/10.1007/s10687-010-0115-5
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