Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on some random orthogonal polynomials on a compact interval
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by Melanie Birke and Holger Dette
Proc. Amer. Math. Soc. 137 (2009), 3511-3522
DOI: https://doi.org/10.1090/S0002-9939-09-09933-X
Published electronically: June 3, 2009

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 $n \to \infty$.
References
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Bibliographic 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
  • 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
  • © Copyright 2009 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 3511-3522
  • MSC (2000): Primary 60F15, 33C45, 44A60
  • DOI: https://doi.org/10.1090/S0002-9939-09-09933-X
  • MathSciNet review: 2515420