Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

Details Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

2009-01-22

arxiv.org/abs/0901.3436v5

Physics

Mathematical Physics

27 pages, 13 figures, 4 tables

Scientific paper

A Toeplitz matrix is one in which the matrix elements are constant along diagonals. The Fisher-Hartwig matrices are much-studied singular matrices in the Toeplitz family. The matrices are defined for all orders, $N$. They are parametrized by two constants, $\alpha$ and $\beta$. Their spectrum of eigenvalues has a simple asymptotic form in the limit as $N$ goes to infinity. Here we study the structure of their eigenvalues and eigenvectors in this limiting case. We specialize to the case $0<\alpha<|\beta|<1$, where the behavior is particularly simple.

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