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

Yeor Hafouta

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arXiv · 2608.02897

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

Yeor Hafouta

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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 \cite{MatBE}. Like in \cite{MatBE} we provide several sufficient conditions for contraction.

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Yeor Hafouta. 2026-08-03. Local limit theorem and Edgeworth expansions for inhomogeneous random walks on $GL(d,\mathbb R)$. https://arxiv.org/abs/2608.02897

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