RANDOM MOMENT PROBLEMS UNDER CONSTRAINTS

• 成果类型: Article
• 署名作者: Dette, Holger; Tomecki, Dominik; Venker, Martin
• 署名单位: Ruhr University Bochum
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1370
• 发表日期: 2020
• 页码: 672-713
• 关键词: large deviations; limit-theorem; distributions

摘要

We investigate moment sequences of probability measures on subsets of the real line under constraints of certain moments being fixed. This corresponds to studying sections of nth moment spaces, that is, the spaces of moment sequences of order n. By equipping these sections with the uniform or more general probability distributions, we manage to give for large n precise results on the (probabilistic) barycenters of moment space sections and the fluctuations of random moments around these barycenters. The measures associated to the barycenters belong to the Bernstein-Szego class and show strong universal behavior. We prove Gaussian fluctuations and moderate and large deviations principles. Furthermore, we demonstrate how fixing moments by a constraint leads to breaking the connection between random moments and random matrices.