Entropically regularized optimal transport (EOT) has emerged as a powerful computational and theoretical tool, yet its small-regularization limit remains subtle, especially in dimensions d>1. In this talk, I will present recent progress on understanding the convergence of EOT to optimal transport in the vanishing regularization regime. Building on ideas from optimal transport geometry and large deviations theory, we quantify the local exponential convergence of entropic optimizers and characterize the exact rate function in terms of the Kantorovich potential. I will then focus on a new selection principle for the Monge transport plan when the cost is the Euclidean distance, and the marginals are absolutely continuous. We show that the limiting plan is supported on transport rays and is uniquely determined within each ray by minimizing a relative entropy functional with respect to a canonical reference measure. This variational characterization provides a complete and unique description of the limiting transport plan.
Back to Long Programs
Copyright. All Rights Reserved.