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March 2020 Random moment problems under constraints
Holger Dette, Dominik Tomecki, Martin Venker
Ann. Probab. 48(2): 672-713 (March 2020). DOI: 10.1214/19-AOP1370

Abstract

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 $n$th 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–Szegő 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.

Citation

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Holger Dette. Dominik Tomecki. Martin Venker. "Random moment problems under constraints." Ann. Probab. 48 (2) 672 - 713, March 2020. https://doi.org/10.1214/19-AOP1370

Information

Received: 1 June 2018; Revised: 1 March 2019; Published: March 2020
First available in Project Euclid: 22 April 2020

zbMATH: 07199858
MathSciNet: MR4089491
Digital Object Identifier: 10.1214/19-AOP1370

Subjects:
Primary: 30E05, 60B20, 60F05

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 2 • March 2020
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