DISTRIBUTIONS ON UNBOUNDED MOMENT SPACES AND RANDOM MOMENT SEQUENCES

• 成果类型: Article
• 署名作者: Dette, Holger; Nagel, Jan
• 署名单位: Ruhr University Bochum; Technical University of Munich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP693
• 发表日期: 2012
• 页码: 2690-2704
• 关键词: asymptotic properties

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.