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Spectral Norm of Circulant-Type Matrices

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Abstract

We first discuss the convergence in probability and in distribution of the spectral norm of scaled Toeplitz, circulant, reverse circulant, symmetric circulant, and a class of k-circulant matrices when the input sequence is independent and identically distributed with finite moments of suitable order and the dimension of the matrix tends to ∞.

When the input sequence is a stationary two-sided moving average process of infinite order, it is difficult to derive the limiting distribution of the spectral norm, but if the eigenvalues are scaled by the spectral density, then the limits of the maximum of modulus of these scaled eigenvalues can be derived in most of the cases.

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Authors and Affiliations

  1. Statistics and Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700108, India

    Arup Bose, Rajat Subhra Hazra & Koushik Saha

Authors
  1. Arup Bose
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  2. Rajat Subhra Hazra
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  3. Koushik Saha
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Corresponding author

Correspondence to Rajat Subhra Hazra.

Additional information

A. Bose’s research supported by J.C. Bose Fellowship, Dept. of Science and Technology, Govt. of India.

K. Saha’s research supported by CSIR Fellowship, Govt. of India.

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Bose, A., Hazra, R.S. & Saha, K. Spectral Norm of Circulant-Type Matrices. J Theor Probab 24, 479–516 (2011). https://doi.org/10.1007/s10959-009-0257-z

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  • DOI: https://doi.org/10.1007/s10959-009-0257-z

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