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Fine Structure of the Zeros of Orthogonal Polynomials: A Progress Report

Simon, Barry (2010) Fine Structure of the Zeros of Orthogonal Polynomials: A Progress Report. In: Recent Trends in Orthogonal Polynomials and Approximation Theory. Contemporary Mathematics . No.507. American Mathematical Society , Providence, RI, pp. 241-254. ISBN 978-0-8218-4803-6.

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We consider the asymptotics of zeros of OPRL and POPUC as n → ∞, focusing on the structure on a scale in x of order 1/n. We discuss three recent results (on Poisson behavior in the random case, clock on the a.c. case, and beta-distribution in between) and open questions and speculations.

Item Type:Book Section
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Simon, Barry0000-0003-2561-8539
Additional Information:© 2010 American Mathematical Society. Supported in part by NSF grant DMS-0652919.
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Subject Keywords:Orthogonal polynomials; clock behavior; Poisson process
Series Name:Contemporary Mathematics
Issue or Number:507
Classification Code:2000 Mathematics Subject Classification: 26C10, 65H17, 05E35
Record Number:CaltechAUTHORS:20100715-092306403
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19066
Deposited By: Tony Diaz
Deposited On:06 Aug 2010 21:39
Last Modified:03 Oct 2019 01:51

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