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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Jonathan Breuer
Journal: Trans. Amer. Math. Soc. 362 (2010), 3161-3182
MSC (2000): Primary 47B36; Secondary 60H25
Published electronically: January 20, 2010
MathSciNet review: 2592951
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-10-04856-7
PII: S 0002-9947(10)04856-7
Received by editor(s): November 13, 2007
Received by editor(s) in revised form: June 16, 2008
Published electronically: January 20, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.