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arXiv · 2512.05034

Analytic Dependence of the Lyapunov Moment Function and the Projective Stationary Measure for Random Matrix Products

Christopher Chalhoub·Vincent P. H. Goverse·Jeroen S. W. Lamb·Martin Rasmussen
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Abstract

We consider the product of i.i.d. random matrices sampled according to a probability measure $\mu$ 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 $\mu$ in the total variation topology. As a consequence, we obtain the analyticity of the asymptotic variance and all higher-order Lyapunov moments.

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Christopher Chalhoub, Vincent P. H. Goverse, Jeroen S. W. Lamb, Martin Rasmussen. 2025-12-04. Analytic Dependence of the Lyapunov Moment Function and the Projective Stationary Measure for Random Matrix Products. https://arxiv.org/abs/2512.05034

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