Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 1

Explore the theory of random matrix products in this advanced mathematics lecture that delves into the long-term behavior of stationary random matrices. Learn about fundamental concepts including Lyapunov exponents and stationary measures while examining the interplay between dynamical systems, ergodic theory, probability theory, and algebraic groups. Discover how this field has evolved from its foundations in the 1960s-70s with Furstenberg, Kesten, Virtzer, and Tutubalin through developments by Guivarc'h, Raugi, Bougerol, Goldsheid, and Margulis in subsequent decades. Gain insights into the classification of stationary probability measures on projective space in the i.i.d case, building on joint research that connects the foundational work of Furstenberg-Kifer with later contributions from Guivarc'h-Raugi and Benoist-Quint.