Dimension of Stationary Measures in Random Walks on Matrix Groups - Lecture Series

Explore the dimension of stationary measures in this comprehensive lecture series from the Simons Semester on Dynamics. Delve into the study of random walks on matrix groups and their actions on flag spaces. Examine the exact dimension of dynamical (Oseledets) measures and investigate partial answers to other related problems. Gain insights into the fine structure of flag spaces and learn about generalities of measure dimension and random walks on matrices. Discover the proof strategy for dimension 3 cases and explore examples of Hitchin representations. Investigate admissible topologies, configuration spaces, and their dynamics. Understand the one-step formula and the relationship between entropy addition and dimension. This 1-hour 2-minute lecture, delivered by François Ledrappier and Pablo Lessa, offers a deep dive into advanced mathematical concepts for researchers and students in the field of dynamical systems.