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arXiv · 1712.03698

Limit laws for random matrix products

Jordan Emme·Pascal Hubert
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Abstract

In this short note, we study the behaviour of a product of matrices with a simultaneous renormalization. Namely, for any sequence $(A\_n)\_{n\in \mathbb{N}}$ of $d\times d$ complex matrices whose mean $A$ exists and whose norms' means are bounded, the product $\left(I\_d + \frac1n A\_0 \right) \dots \left(I\_d + \frac1n A\_{n-1} \right) $ converges towards $\exp{A}$. We give a dynamical version of this result as well as an illustration with an example of "random walk" on horocycles of the hyperbolic disc.

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Jordan Emme, Pascal Hubert. 2017-12-11. Limit laws for random matrix products. https://arxiv.org/abs/1712.03698

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