Spectral and dynamical properties of certain random Jacobi matrices with growing parameters
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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.References
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Additional Information
- Jonathan Breuer
- Affiliation: Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
- Address at time of publication: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
- Email: jbreuer@caltech.edu
- Received by editor(s): November 13, 2007
- Received by editor(s) in revised form: June 16, 2008
- Published electronically: January 20, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 3161-3182
- MSC (2000): Primary 47B36; Secondary 60H25
- DOI: https://doi.org/10.1090/S0002-9947-10-04856-7
- MathSciNet review: 2592951