A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group

被引：5

作者：

Grama, Ion ^{[1
]}

Quint, Jean-Francois ^{[2
]}

Xiao, Hui ^{[3
]}

机构：

[1] Univ Bretagne Sud, CNRS UMR LMBA 6205, Campus Tohann, F-56017 Vannes, France

[2] Univ Bordeaux, CNRS, IMB, Bordeaux INP, F-33400 Talence, France

[3] Univ Hildesheim, Inst Math & Angew Informat, Hildesheim, Germany

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2022年 / 58卷 / 04期

关键词：

General linear group; Zero-one law; Stationary measure; Random matrices; Regularity; Algebraic set; SPECTRAL GAP PROPERTIES; STATIONARY MEASURES; PRODUCTS; ASYMPTOTICS;

D O I：

10.1214/21-AIHP1221

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 Poincare 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.

引用

页码：2321 / 2346

页数：26

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