Berry-Essén theorem for random determinants

Malliavin derivative; Multiple stochastic integrals; Random determinant; Random matrix; Statistics and Probability; Statistics, Probability and Uncertainty

Abstract :

[en] Let Xn be a n×n random matrix with independent Gaussian entries. Then it is well-known that log(|det(Xn|)) satisfies a Central Limit Theorem. Our purpose is to evaluate the 1-Wasserstein distance for this limit theorem via the techniques of the Stein–Malliavin calculus.

Disciplines :

Mathematics

Author, co-author :

DIEZ, Charles-Philippe Manuel ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; CNRS, Université de Lille, Laboratoire Paul Painlevé UMR 8524, Villeneuve d'Ascq, France

Tudor, Ciprian A.; CNRS, Université de Lille, Laboratoire Paul Painlevé UMR 8524, Villeneuve d'Ascq, France

External co-authors :

yes

Language :

English

Title :

Berry-Essén theorem for random determinants

Publication date :

June 2023

Journal title :

Statistics and Probability Letters

ISSN :

0167-7152

Publisher :

Elsevier B.V.

Volume :

197

Pages :

109804

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0167715223000287?httpAccept=text/xml

Funding text :

C. Tudor acknowledges partial support from Labex CEMPI ( ANR-11-LABX-007-01 ), the ANR project ANR-22-CE40-0015 (SDAIM), the MATHAMSUD (project 22- MATH-08), ECOS SUD (project C2107) and by the Ministry of Research, Innovation and Digitalization (Romania), CNCS-UEFISCDI (grant PN-III-P4-PCE-2021-0921 , within PNCDI III).

Available on ORBilu :

since 30 November 2023

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