01/25: Lewis Bowen

Abstract: In 1960, Furstenberg and Kesten introduced the problem of describing the asymptotic behavior of products of random matrices as the number of factors tends to infinity. Oseledets’ proved that such products, after normalization, converge almost surely. This theorem has wide-ranging applications to smooth ergodic theory and rigidity theory. It has been generalized to products of random operators on Banach spaces by Ruelle and others. I will explain a new infinite-dimensional generalization based on von Neumann algebra theory which accommodates continuous Lyapunov distribution. This will be a gentle introductory-style talk; no knowledge of von Neumann algebras will be assumed. This is joint work with Ben Hayes (U. Virginia) and Yuqing Frank Lin (Ben-Gurion U.).