Gradient estimates for the Schrödinger potentials and convergence to the Brenier map
speaker: Luca Tamanini (Università Bocconi, Milano)abstract: The classical Schrödinger problem consists in finding the most likely evolution of a system of independent Brownian particles conditionally on the observation of the system configuration at two deterministic times. If one assumes a very large number of particles, the resulting evolution can be recast (via large deviations) as an entropy minimization problem. Although it dates back to 1931, it is only in the last decade that this problem has gained a great success, thanks to its interpretation as "noised" optimal transport and the related computational applications. In this talk, after introducing the Schrödinger problem, we discuss the convergence of the gradients of the Schrödinger potentials to the Brenier map in the small-time limit. In this respect, a very general gradient estimate for the Schrödinger potentials plays a fundamental role. If time allows, we will mention a second application of the gradient bound to novel quantitative stability estimates for the optimal values and couplings for the Schrödinger problem. (based on a joint work with A. Chiarini, G. Conforti, and G. Greco)
timetable:
Mon 24 Oct, 17:15 - 17:40, Aula Magna Bruno Pontecorvo
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