Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 3

Explore a lecture on random matrix products focusing on stationary probability measures in projective space, part of the Simons Semester on Dynamics series. Delve into the theory of random matrix products and their long-term behavior, examining products Xn · · · X1 with Xi's stationary random matrices of fixed dimension. Learn about the historical development of this field from its origins with Furstenberg, Kesten, Virtzer, and Tutubalin in the 1960s-70s, through contributions by Guivarc'h, Raugi, Bougerol, Goldsheid, and Margulis in subsequent decades. Discover the fascinating intersection of dynamical systems, ergodic theory, probability theory, and algebraic groups, including recent applications in homogeneous dynamics inspired by Benoist-Quint's work. Master fundamental concepts such as Lyapunov exponents and stationary measures, leading to a comprehensive classification of stationary probability measures on projective space for i.i.d. cases, bridging seminal works by Furstenberg-Kifer, Guivarc'h-Raugi, and Benoist-Quint.