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Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior

Last, Yoram and Simon, Barry (2008) Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior. Communications on Pure and Applied Mathematics, 61 (4). pp. 486-538. ISSN 0010-3640. doi:10.1002/cpa.20185.

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We prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions (Jacobi parameters approach the free ones and are of bounded variation). We prove that for ergodic discrete Schrödinger operators, Poisson behavior implies a positive Lyapunov exponent. Both results depend on a priori bounds on eigenvalue spacings for which we provide several proofs.

Item Type:Article
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URLURL TypeDescription DOIArticle Paper
Simon, Barry0000-0003-2561-8539
Additional Information:© 2007 Wiley Periodicals, Inc. Received: May 2006; published online: 30 Apr 2007. Supported in part by The Israel Science Foundation (Grant No. 188/02). Supported in part by NSF grant DMS-0140592. Research supported in part by Grant No. 2002068 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.
Funding AgencyGrant Number
Israel Science Foundation188/02
Binational Science Foundation (USA-Israel)2002068
Issue or Number:4
Record Number:CaltechAUTHORS:20091016-144551584
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16374
Deposited On:18 Oct 2009 23:31
Last Modified:08 Nov 2021 23:26

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