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November 2012 Distributions on unbounded moment spaces and random moment sequences
Holger Dette, Jan Nagel
Ann. Probab. 40(6): 2690-2704 (November 2012). DOI: 10.1214/11-AOP693

Abstract

In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces and as distributions corresponding to random spectral measures associated with the Jacobi, Laguerre and Hermite ensemble from random matrix theory. For random vectors on the unbounded moment spaces we prove a central limit theorem where the centering vectors correspond to the moments of the Marchenko–Pastur distribution and Wigner’s semi-circle law.

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Holger Dette. Jan Nagel. "Distributions on unbounded moment spaces and random moment sequences." Ann. Probab. 40 (6) 2690 - 2704, November 2012. https://doi.org/10.1214/11-AOP693

Information

Published: November 2012
First available in Project Euclid: 26 October 2012

zbMATH: 1255.60032
MathSciNet: MR3050514
Digital Object Identifier: 10.1214/11-AOP693

Subjects:
Primary: 15B52 , 30E05 , 60F05

Keywords: canonical moments , Gaussian ensemble , Jacobi ensemble , Laguerre ensemble , Marcenko–Pastur distribution , Moment spaces , random moment sequences , Wigner’s semicircle law

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 6 • November 2012
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