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

Published 2020-09-24Version 1

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.