Proceedings of the American Mathematical Society

Author(s): Melanie Birke; Holger Dette
Journal: Proc. Amer. Math. Soc. 137 (2009), 3511-3522.
MSC (2000): Primary 60F15, 33C45, 44A60
Posted: 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

. To each (random) vector of moments in $\mathcal{M}_{2n-1}$ we consider the corresponding uniquely determined monic (random) orthogonal polynomial of degree

and study the asymptotic properties of its roots if $n \to \infty$ .

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 60F15, 33C45, 44A60

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: 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
Posted: 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 of article: Copyright 2009, American Mathematical Society

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