Local limit theorem and Edgeworth expansions for inhomogeneous random walks on GL(d,\mathbb R)

2026/08/03 by Yeor Hafouta
Mathematics · #math.PR #math.DS

paper · pdf

19 pp

arxiv created 2026/08/03 · arxiv updated 2026/08/05

Abstract

We prove a non-lattice local central limit theorem and Edgeworth expansions for the logarithm of the norms of products of invertible independent random matrices. Our conditions include a contraction assumption, an assumption that supports of the matrices are ``large enough" and their distributions are sufficiently regular. As a byproduct of the proof we are also able to provide a different proof to the optimal rates in the CLT proved in \citeMatBE. Like in \citeMatBE we provide several sufficient conditions for contraction.

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