Analytic Dependence of the Lyapunov Moment Function and the Projective Stationary Measure for Random Matrix Products
Authors
Christopher Chalhoub
Vincent P. H. Goverse
Jeroen S. W. Lamb
Martin Rasmussen
Abstract
We consider the product of i.i.d. random matrices sampled according to a probability measure $μ$ supported on a strongly irreducible and proximal subset of a compact set $S\subset GL(d,\mathbb{R})$. We establish the local analyticity of the Lyapunov moment function and the unique stationary measure on the projective space with respect to $μ$ in the total variation topology. As a consequence, we obtain the analyticity of the asymptotic variance and all higher-order Lyapunov moments.
