Spectral measures of Jacobi operators with random potentials

2009/07/11 by Rafael del Rio, del Rio, Rafael, Luis O. Silva +1
Mathematics · Physics and Astronomy · #47A25 #47B36 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:47A25 #msc:47B36

paper · pdf · doi:10.48550/arxiv.0907.1934

15 pages; references updated; typos corrected

arxiv created 2010/01/29 · arxiv updated 2010/02/08

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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