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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on some random orthogonal polynomials on a compact interval


Authors: Melanie Birke and Holger Dette
Journal: Proc. Amer. Math. Soc. 137 (2009), 3511-3522
MSC (2000): Primary 60F15, 33C45, 44A60
Published electronically: June 3, 2009
MathSciNet review: 2515420
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a uniform distribution on the set $ \mathcal{M}_k$ of moments of order $ k \in \mathbb{N}$ corresponding to probability measures on the interval $ [0,1]$. To each (random) vector of moments in $ \mathcal{M}_{2n-1}$ we consider the corresponding uniquely determined monic (random) orthogonal polynomial of degree $ n$ and study the asymptotic properties of its roots if $ n \to \infty$.


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Additional Information

Melanie Birke
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany
Email: melanie.birke@rub.de

Holger Dette
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany
Email: holger.dette@rub.de

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09933-X
PII: S 0002-9939(09)09933-X
Keywords: Moment space, random moment sequence, random orthogonal polynomial, arcsine distribution, Chebyshev polynomials, random matrices
Received by editor(s): June 20, 2008
Received by editor(s) in revised form: February 19, 2009
Published electronically: June 3, 2009
Additional Notes: The authors are grateful to Martina Stein, who typed most of this paper with considerable technical expertise. The work of the authors was supported by the Sonderforschungsbereich Tr/12, Fluctuations and universality of invariant random matrix ensembles (project C2), and in part by an NIH grant award IR01GM072876:01A1.
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2009 American Mathematical Society