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

Jonathan Breuer

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

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

Jonathan Breuer^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	American English
Pages (from-to)	3161-3182
Number of pages	22
Journal	Transactions of the American Mathematical Society
Volume	362
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9947-10-04856-7
State	Published - Jun 2010

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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 Schr{\"o}dinger 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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AB - 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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Spectral and dynamical properties of certain random jacobi matrices with growing parameters

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