arXiv 1007.33692010-07math.PR

Distributions on unbounded moment spaces and random moment sequences

Holger Dette, Jan Nagel

备注：: Published in at http://dx.doi.org/10.1214/11-AOP693 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
发表信息：: Annals of Probability 2012, Vol. 40, No. 6, 2690-2704
DOI：: 10.1214/11-AOP693

英文摘要：

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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