Noncommuting random products
Time and place
1 PM on Thursday, October 4th, 2012; NAC 6/113
Anders Karlsson (University of Geneva)
Abstract
In a seminal paper from 1963 Furstenberg inquired to what extent the law of large numbers in probability extends to a noncommutative setting when the random variables take values in a group more general than the additive reals. Questions related to this have been studied extensively over the years. Applications can notably be found in the theory of smooth dynamical systems, in difference equations with random coefficients and in Margulis' proof of superrigidity and arithmeticity for higher rank lattices in Lie groups.
I will present a relatively recent and general such noncommutative ergodic theorem obtained in a joint work with F. Ledrappier. I will outline a few of its applications, for example to Brownian motion and harmonic functions on Riemannian manifolds, or to an extension of the spectral theorem for surface homeomorphisms due to Thurston.
