November 2022 A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group
Ion Grama, Jean-François Quint, Hui Xiao
Author Affiliations +
Ann. Inst. H. Poincaré Probab. Statist. 58(4): 2321-2346 (November 2022). DOI: 10.1214/21-AIHP1221

Abstract

We prove a zero-one law for the stationary measure for algebraic sets generalizing the results of Furstenberg (Proc. Sympos. Pure Math. 26 (1973) 193–229) and Guivarc’h and Le Page (Ann. Inst. Henri Poincaré Probab. Stat. 52(2) (2016) 503–574). As an application, we establish a local limit theorem for the coefficients of random walks on the general linear group.

Nous prouvons une loi zéro-un pour la mesure stationnaire pour des ensembles algébriques en généralisant les résultats de Furstenberg (Proc. Sympos. Pure Math. 26 (1973) 193–229) et Guivarc’h et Le Page (Ann. Inst. Henri Poincaré Probab. Stat. 52(2) (2016) 503–574). Comme application, nous établissons un théorème local limite pour les coefficients de marches aléatoires sur le groupe linéaire général.

Acknowledgments

The authors would like to thank an anonymous referee for the careful reading of the paper.

Hui Xiao is corresponding author.

Citation

Download Citation

Ion Grama. Jean-François Quint. Hui Xiao. "A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group." Ann. Inst. H. Poincaré Probab. Statist. 58 (4) 2321 - 2346, November 2022. https://doi.org/10.1214/21-AIHP1221

Information

Received: 24 September 2020; Revised: 26 September 2021; Accepted: 14 October 2021; Published: November 2022
First available in Project Euclid: 6 October 2022

MathSciNet: MR4492980
zbMATH: 1505.37015
Digital Object Identifier: 10.1214/21-AIHP1221

Subjects:
Primary: 15B52 , 37A30 , 60B15
Secondary: 60B20

Keywords: Algebraic set , general linear group , random matrices , regularity , stationary measure , Zero-one law

Rights: Copyright © 2022 Association des Publications de l’Institut Henri Poincaré

JOURNAL ARTICLE
26 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.58 • No. 4 • November 2022
Back to Top