Random Matrix Products: Stationary Probability Measures on the Projective Space - Lecture 2

Explore a lecture on random matrix products theory, focusing on stationary probability measures in projective space. Delve into the historical development of this field from its origins with Furstenberg, Kesten, Virtzer, and Tutubalin in the 1960-70s through its evolution with Guivarc'h, Raugi, Bougerol, Goldsheid, and Margulis in subsequent decades. Learn about the fundamental tools essential for studying random matrix products, including Lyapunov exponents and stationary measures, while examining their properties. Discover the complete classification of stationary probability measures on the projective space of natural Markov chains induced by these products in the i.i.d case, based on joint research with C. Sert that connects the foundational work of Furstenberg-Kifer with that of Guivarc'h-Raugi and Benoist-Quint. Understand how this field combines elements from dynamical systems, ergodic theory, probability theory, and algebraic groups, particularly in its modern applications to homogeneous dynamics.