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arXiv · 2009.11593

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 [13] and Guivarc'h and Le Page [20]. As an application, we establish a local limit theorem for the coefficients of random walks on the general linear group.

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Ion Grama, Jean-François Quint, Hui Xiao. 2020-09-24. A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group. https://doi.org/10.1214/21-aihp1221

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