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Published June 2010 | Published
Journal Article Open

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

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 Dumitriu-Edelman model (2002), and its spectral properties are analyzed

Additional Information

© 2010 American Mathematical Society. Reverts to public domain 28 years from publication. Received by editor(s): November 13, 2007. Received by editor(s) in revised form: June 16, 2008. Posted: January 20, 2010. We are grateful to Peter Forrester and Uzy Smilansky for presenting us with the problem that led to this paper. We also thank Yoram Last and Uzy Smilansky for many useful discussions. We thank the referee for helpful remarks. This research was supported in part by THE ISRAEL SCIENCE FOUNDATION (grant no. 1169/06) and by grant no. 2002068 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.

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