Spectral measures of Jacobi operators with random potentials

Details Spectral measures of Jacobi operators with random potentials Spectral measures of Jacobi operators with random potentials

2009-07-11

arxiv.org/abs/0907.1934v2

Physics

Mathematical Physics

15 pages; references updated; typos corrected

Scientific paper

Let $H_\omega$ be a self-adjoint Jacobi operator with a potential sequence $\{\omega(n)\}_n$ of independently distributed random variables with continuous probability distributions and let $\mu_\phi^\omega$ be the corresponding spectral measure generated by $H_\omega$ and the vector $\phi$. We consider sets $A(\omega)$ which depend on $\omega$ in a particular way and prove that $\mu_\phi^\omega(A(\omega))=0$ for almost every $\omega$. This is applied to show equivalence relations between spectral measures for random Jacobi matrices and to study the interplay of the eigenvalues of these matrices and their submatrices.

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