Singular components of spectral measures for ergodic Jacobi matrices
Spectral Theory
2015-05-27 v2
Abstract
For ergodic 1d Jacobi operators we prove that the random singular components of any spectral measure are almost surely mutually disjoint as long as one restricts to the set of positive Lyapunov exponent. In the context of extended Harper's equation this yields the first rigorous proof of the Thouless' formula for the Lyapunov exponent in the dual regions.
Cite
@article{arxiv.1104.3376,
title = {Singular components of spectral measures for ergodic Jacobi matrices},
author = {C. A. Marx},
journal= {arXiv preprint arXiv:1104.3376},
year = {2015}
}
Comments
to appear in the Journal of Mathematical Physics, vol 52 (2011)