MPEJ Volume 13, No. 5, 40 pp.
Received: Mar 1, 2007. Revised: Aug 14, 2007. Accepted: Sep 20, 2007.
H.Schulz-Baldes
Rotation numbers for Jacobi matrices with matrix entries
ABSTRACT: A Jacobi matrix with matrix entries is a selfadjoint block
tridiagonal matrix with positive definite blocks on the off-diagonals.
A rotation number calculation for its eigenvalues is presented. This is a
matricial generalization of the oscillation theorem for the discrete analogues
of Sturm-Liouville operators. The three universality classes of time reversal
invariance are dealt with by implementing the corresponding symmetries. For
Jacobi matrices with random matrix entries, this leads to a formula for the
integrated density of states which can be calculated perturbatively in the
coupling constant of the randomness with an optimal control on the error terms.
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