Stability and Limit Laws of Stochastic Optimal Transport Maps

Explore the mathematical foundations of stochastic optimal transport through this conference talk that examines stability properties and limit laws governing optimal transport maps in probabilistic settings. Delve into the theoretical framework where optimal transport theory intersects with stochastic processes, learning how transport maps behave under various probabilistic conditions and what convergence properties they exhibit. Investigate the stability characteristics of these maps when subjected to random perturbations and understand the limiting behavior as system parameters change. Examine rigorous mathematical proofs and theoretical results that establish when and how stochastic optimal transport maps converge, providing essential insights for applications in machine learning, economics, and statistical inference where randomness plays a crucial role in transportation problems.