Title: “Random matrix products: limit theorems and stationary measures”.

 

Abstract: Random matrix products theory has known  deep contributions in the last few years due to its large spectrum of applications: expander graphs, geometric group theory, diophantine approximation… 

Roughly speaking, its goal is to study the behavior of a random walk on the general linear group GL(V) where V is a finite dimensional vector space. 

 

 

The goal of the talk is to give an overview of the theory, present the standard tools needed to study it (Lyapunov exponents, stationary measures, …) and to give recent results in this theory (limit theorems, results in the non-irreducible setting, …). Part of the results I will talk about are joint works with C. Sert and Y. Guivarc’h.