Dimension of Stationary Measures - Lecture 4

Explore the fourth lecture in a series on the dimension of stationary measures for random walks, presented by François Ledrappier and Pablo Lessa. Delve into the study of matrix group actions on flag spaces, examining exact dimension proofs for dynamical Oseledets measures and partial answers to related problems. Investigate the fine structure of flag spaces to gain deeper insights. Learn about change of coordinates and dynamics of configuration spaces, as well as the one-step formula. Conclude with a discussion on the addition of entropy and dimension, building upon previous lectures covering generalities about measure dimensions, random walks on matrices, and strategies for proofs in three-dimensional cases.

François Ledrappier / Pablo Lessa ( CNRS / Universidad de la República, Uruguay), lecture 4