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arXiv · 0907.1934

Spectral measures of Jacobi operators with random potentials

Rafael del Rio·Luis O. Silva
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Abstract

Let $H_ω$ be a self-adjoint Jacobi operator with a potential sequence $\{ω(n)\}_n$ of independently distributed random variables with continuous probability distributions and let $μ_ϕ^ω$ be the corresponding spectral measure generated by $H_ω$ and the vector $ϕ$. We consider sets $A(ω)$ which depend on $ω$ in a particular way and prove that $μ_ϕ^ω(A(ω))=0$ for almost every $ω$. 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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Rafael del Rio, Luis O. Silva. 2010-01-29. Spectral measures of Jacobi operators with random potentials. https://arxiv.org/abs/0907.1934

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