04/13: Cagri Sert

Extremal behaviour and spectral radius of random products of matrices

Abstract: I will survey some recent progress on random matrix products theory. In a first part, I will talk about some rigidity phenomenon for the laws of random products exhibiting an extremal behaviour (e.g. fastest possible norm growth). In a second part, I will focus on spectral radius of random products and mention two recent limit theorems: law of large numbers (without irreducibility condition), and for rank one groups, large deviation principle.

Based on joint works with Richard Aoun, Jairo Bochi, Emmanuel Breuillard and Alessandro Sisto.