Journal of Theoretical Probability

, Volume 24, Issue 2, pp 479–516 | Cite as

Spectral Norm of Circulant-Type Matrices

  • Arup Bose
  • Rajat Subhra Hazra
  • Koushik Saha


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.


Large-dimensional random matrix Eigenvalues Toeplitz matrix Hankel matrix Circulant matrix Symmetric circulant matrix Reverse circulant matrix k-circulant matrix Spectral norm Moving average process Spectral density Normal approximation 

Mathematics Subject Classification (2000)

15A52 60F99 60F05 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Statistics and Mathematics UnitIndian Statistical InstituteKolkataIndia

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