Limit laws for random matrix products

11 Dec 2017  ·  Emme Jordan FRUMAM, I2M, Hubert Pascal ·

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. read more

PDF Abstract
No code implementations yet. Submit your code now

Categories


Dynamical Systems Probability