Abstract
Let Hω be a self-adjoint Jacobi operator with a potential sequence {ω(n)}n of independently distributed random variables with continuous probability distributions and let μφ be the corresponding spectral measure generated by Hω and the vector φ. We consider sets A(ω) which depend on ω, but are independent of two consecutive given entries of the secuence ω, and prove that μφ(A(ω)) = 0 for almost every ω. This result 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. This is based on joint work with Luis Silva.
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