Title: An equilibrium problem for the limiting eigenvalue distribution of banded Toeplitz matrices Authors: Duits, MauriceKuijlaars, Arno # × Issue Date: 2008 Publisher: Society for Industrial and Applied Mathematics Series Title: SIAM journal on matrix analysis and applications vol:30 issue:1 pages:173-196 Abstract: We study the limiting eigenvalue distribution of $n \times n$ banded Toeplitz matrices as $n \rightarrow \infty$. 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 $n \rightarrow \infty$. 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 minimizes an energy functional defined on admissible vectors of measures. In addition, we show that each of the other components is the limiting measure of the normalized counting measure on certain generalized eigenvalues. ISSN: 0895-4798 Publication status: published KU Leuven publication type: IT Appears in Collections: Analysis Section