From martingale optimal transport to diffusive transport distances

par Aymeric Baradat

mercredi 4 mars 2026, 10:00 → 12:00 Europe/Paris

112 (Braconnier)

In this talk, we show that martingale optimal transport induces a natural notion of arc length for sufficiently regular continuous-time martingales. This arc length admits a Benamou–Brenier-type formulation, in which the continuity equation is replaced by a diffusion equation. As a consequence, certain PDEs, such as the Derrida–Lebowitz–Speer–Spohn (DLSS) equation, can be interpreted as gradient flows with respect to metrics arising from martingale optimal transport. This talk is mainly based on the paper “A Benamou–Brenier formulation of martingale optimal transport” by Huesmann and Trevisan.