Band Edge Behavior of the Integrated Density of States of Random Jacobi Matrices in Dimension 1

Let H be a Jacobi matrix acting on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\ell ^2 (\mathbb{Z})$$ \end{document} and Vω a random potential of Anderson type. Let Hω = H+Vω. We give a general formula relating the decay of the integrated density of states of Hω at the edges of the almost sure spectrum of Hω to the decay of the integrated density of states of H at the edges of the spectrum of H.