PROBABILITY SPECTRUM OF RANDOM TOEPLITZ MATRICES WITH BAND STRUCTURE

@inproceedings{Kargin2009PROBABILITYSO,
  title={PROBABILITY SPECTRUM OF RANDOM TOEPLITZ MATRICES WITH BAND STRUCTURE},
  author={Vladislav Kargin},
  year={2009}
}
This paper considers the eigenvalues of symmetric Toeplitz matrices with independent random entries and band structure. We assume that the entries of the matrices have zero mean and a uniformly bounded 4th moment, and we study the limit of the eigenvalue distribution when both the size of the matrix and the width of the band with non-zero entries grow to infinity. It is shown that if the bandwidth/size ratio converges to zero, then the limit of the eigenvalue distributions is Gaussian. If the… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-8 of 8 references

Limiting spectral distribution of a special circulant

  • A. Bose, J. Mitra
  • Statistics and Probability Letters,
  • 2002
Highly Influential
3 Excerpts

Time Series: Theory and Methods

  • P. J. Brockwell, R. A. Davis
  • Springer Series in Statistics. Springer-Verlag…
  • 1991
Highly Influential
2 Excerpts

The variation of the spectrum of a normal matrix

  • A. J. Hoffman, H. W. Wielandt
  • Duke Mathematical Journal,
  • 1953
Highly Influential
3 Excerpts