2017/12/11 by Emme, Jordan, Hubert, Pascal
#Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1712.03698
In this short note, we study the behaviour of a product of matrices with a simultaneous renormalization. Namely, for any sequence (A_n)_n∈ ℕ of d× d complex matrices whose mean A exists and whose norms' means are bounded, the product (I_d + \frac1n A_0 ) … (I_d + \frac1n A_n-1 ) converges towards expA. 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.