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
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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