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Event Details
CAMS Seminar: Random matrix products when the top Lyapunov exponent is simple.

Date: October-11-2017 03:00 PM till October-11-2017 04:00 PM
Location: College Hall, Center for Advanced Mathematical Sciences, Room 416
Contact Person: CAMS , hh47@aub.edu.lb
Category: Seminar

The Center For Advanced Mathematical Sciences invites you to a seminar entitled "Random matrix products when the top Lyapunov exponent is simple" by Richard Aoun, AUB.

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 defined on any local field. 

Fine results are known provided the law μ of the increments satisfies some algebraic assumption on the support of μ (irreducibility) and some dynamical assumption (proximality). In this talk, we present new results concerning this theory obtained with Pr. Yves Guivarc’h. In this work, we keep a dynamical assumption but consider no algebraic assumption on the support of μ. We show that this settings leads to new dynamics, essentially on a skew-product space. We show that there exists a unique stationary probability measure ν on the projective space of V corresponding to the top Lyapunov exponent. We describe the support of ν in terms of μ and relate it to the limit set of the semi-group of GL(V ) generated by the support of μ. Furthermore, we show that ν has Holder regularity and give new applications to random walks on the affine group.

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