Dipartimento di Matematica ''F. Casorati''

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Regular approximation of Wasserstein geodesics via entropy minimization

Dr. Luca Tamanini, Institut für Angewandte Mathematik, Bonn

Sala conferenze IMATI-CNR Pavia - Giovedì 5 Aprile 2018 h.15:00

Abstract. How can we approximate Wasserstein geodesics in a smooth and efficient way? Aim of the talk is to answer this question by presenting the Schrödinger problem in its many different formulations and its deep connection with optimal transport. For this reason, in the first part we will resume the basic notions and facts in transportation theory. In the second part a similar picture for the Schrödinger problem will be provided, emphasizing analogies and differences between the two problems, both at physical and mathematical level. A crucial role will be played by entropic interpolations and Schrödinger potentials, approximating counterparts of Wasserstein geodesics and Kantorovich potentials. We will investigate their regularity and point out the uniform estimates that enable to recover optimal transport as limit of (suitably rescaled) Schrödinger problems.
If time permits, an application of this approximation procedure within the framework of RCD spaces will be given.
The talk is based on two joint works with prof. Nicola Gigli.

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Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
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