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Explore the dimension of stationary measures in this advanced mathematics lecture from the Simons Semester on Dynamics. Delve into the study of random walks on matrix groups acting on flag spaces, examining exact dimension proofs for dynamical Oseledets measures and partial answers to related problems. Investigate the fine structure of flag spaces, generalities about measure dimensions, and random walks on matrices. Learn about the proof strategy in three dimensions, including examples of Hitchin representations. Examine admissible topologies, configuration spaces, coordinate changes, and their dynamics. Understand the one-step formula and the relationship between entropy addition and dimension in this comprehensive exploration of stationary measure dimensions.
