An Equilibrium Problem for the Limiting Eigenvalue Distribution of Banded Toeplitz Matrices

@article{Duits2008AnEP,
  title={An Equilibrium Problem for the Limiting Eigenvalue Distribution of Banded Toeplitz Matrices},
  author={Maurice Duits and Arno B. J. Kuijlaars},
  journal={SIAM J. Matrix Analysis Applications},
  year={2008},
  volume={30},
  pages={173-196}
}
We study the limiting eigenvalue distribution of n×n banded Toeplitz matrices as n → ∞. From classical results of Schmidt-Spitzer and Hirschman it is known that the eigenvalues accumulate on a special curve in the complex plane and the normalized eigenvalue counting measure converges weakly to a measure on this curve as n → ∞. In this paper, we characterize the limiting measure in terms of an equilibrium problem. The limiting measure is one component of the unique vector of measures that… CONTINUE READING

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