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
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
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