BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

When Otto meets Newton and Schrödinger, an heuristic point of view Gentil, Ivan


We propose a generalization of the Schr\"odinger problem by replacing the usual entropy with a functional $\mathcal F$ which approaches the Wasserstein distance along the gradient of $\mathcal F$. From an heuristic point of view by using Otto calculus, we show that interpolations satisfy a Newton equation, extending the recent result of Giovani Conforti. Various inequalities as Evolutional-Variational-inequalities are also established from a heuristic point of view. As a rigorous result we prove a new and general contraction inequality for the usual Schr\"odinger problem under Ricci bound on a smooth and compact Riemannian manifold. This is a joint work with L. Ripani and C. L\'eonard.

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