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Spectral and Dynamical Properties of Certain Random Jacobi Matrices with Growing Parameters

Authors
  • Breuer, Jonathan
Type
Preprint
Publication Date
Jun 16, 2008
Submission Date
Aug 05, 2007
Source
arXiv
License
Yellow
External links

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 Schr\"odinger 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 Gaussian $\beta$ Ensembles and their spectral properties are analyzed.

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