Schrödinger Bridges: Old and New - Part 1

This lecture, presented by Tryphon Georgiou from the University of California, Irvine, explores the mathematical concept of Schrödinger Bridges in the first part of a two-lecture series at IPAM's Non-commutative Optimal Transport Tutorials. Delve into the groundbreaking work initiated by Erwin Schrödinger in his 1931 paper "Über die Umkehrung der Naturgesetze" (On the Reversal of the Laws of Nature), which examines time reversal in diffusion processes and the implications of conditioning these processes with specified marginals at different time points. Discover how Schrödinger's ideas connect various concepts including relative entropy between probability laws, likelihood estimation, large deviations theory, stochastic optimization, and Monge-Kantorovich optimal mass transport. This first lecture focuses on presenting key theoretical aspects and applications of classical Schrödinger bridges, setting the foundation for the non-commutative counterparts that will be covered in the second part of the series. Recorded on March 11, 2025, this 82-minute presentation is part of UCLA's Institute for Pure & Applied Mathematics programming.