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arXiv · 2607.19873

Local limit theorem for the operator norm of products of random matrices

Ion Grama·Jean-François Quint·Hui Xiao
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Abstract

We prove a local limit theorem for the quantity $\| g_n \cdots g_1 \|$, where $g_1, g_2, \ldots$ is a sequence of independent and identically distributed random invertible square matrices. The norm $\| \cdot \|$ is arbitrary and we make no proximality assumption.

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Ion Grama, Jean-François Quint, Hui Xiao. 2026-07-22. Local limit theorem for the operator norm of products of random matrices. https://arxiv.org/abs/2607.19873

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