Geometric study of Wasserstein spaces and free probability
The proposed research is divided into two main work packages. The first one is the study of spaces of measures equipped with the optimal transport distance (Wasserstein distance) with a special emphasis on the structure of isometr...
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Información proyecto GWFP
Duración del proyecto: 29 meses
Fecha Inicio: 2019-04-10
Fecha Fin: 2021-09-30
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Descripción del proyecto
The proposed research is divided into two main work packages. The first one is the study of spaces of measures equipped with the optimal transport distance (Wasserstein distance) with a special emphasis on the structure of isometries (surjective distance-preserving maps) and isometric embeddings (not necessarily surjective transformations that preserve the distance) of these spaces. The second work package is devoted to the investigation of measures from the viewpoint of free probability theory. This work package covers three subtopics: the qualitative behaviour of the free convolution, new random matrix ensembles arising from tensor networks, and the study of free Wasserstein spaces.