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This lecture explores the convergence properties and geometric aspects of Entropically Regularized Optimal Transport (EOT), presented by Promit Ghosal from the University of Chicago at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Delve into recent advances in understanding how EOT converges to optimal transport when regularization approaches zero, particularly challenging in higher dimensions. Learn about the quantification of local exponential convergence of entropic optimizers and the characterization of exact rate functions using Kantorovich potentials. Discover a novel selection principle for Monge transport plans with Euclidean distance costs and absolutely continuous marginals, showing how the limiting plan is supported on transport rays and uniquely determined by minimizing relative entropy with respect to a canonical reference measure. This 58-minute presentation offers valuable insights into the mathematical foundations that make EOT a powerful computational and theoretical tool in transport theory.
