Spectral and dynamical properties of certain random Jacobi matrices with growing parameters

Breuer, Jonathan

doi:10.1090/S0002-9947-10-04856-7

Spectral and dynamical properties of certain random Jacobi matrices with growing parameters
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Trans. Amer. Math. Soc. 362 (2010), 3161-3182 Request permission

Abstract:

In this paper, a family of random Jacobi matrices with off-diagonal terms that exhibit power-law growth is studied. Since the growth of the randomness is slower than that of these terms, it is possible to use methods applied in the study of Schrödinger operators with random decaying potentials. A particular result of the analysis is the existence of operators with arbitrarily fast transport whose spectral measure is zero dimensional. The results are applied to the infinite Dumitriu-Edelman model (2002), and its spectral properties are analyzed.

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