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

doi:10.1214/21-AIHP1221

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

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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.

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Ion Grama, Jean-François Quint, and Hui Xiao "A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group," Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 58(4), 2321-2346, (November 2022). https://doi.org/10.1214/21-AIHP1221

Received: 24 September 2020; Accepted: 14 October 2021; Published: November 2022

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