Optimal Transport and High-Dimensional Probability

Explore the connections between optimal transport theory and high-dimensional probability in this 57-minute lecture by Yair Shenfeld from Brown University. Delve into functional inequalities, including the log-Sobolev inequality and Talagrand's inequality, and examine their role in the convergence of flows. Investigate the concepts of displacement convexity and logconcavity of probability measures, gaining insights into the interplay between optimal transport techniques and probabilistic phenomena in high-dimensional spaces.