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

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.

References in corpus (2)

• Large deviation expansions for the coefficients of random walks on the general linear group
• Moderate deviations and local limit theorems for the coefficients of random walks on the general linear group

Cited by in corpus (3)

• Large deviation expansions for the coefficients of random walks on the general linear group
• Berry-Esseen bound and Local Limit Theorem for the coefficients of products of random matrices
• Random walks on SL_2(C): spectral gap and limit theorems