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Geometric study of Wasserstein spaces and free probability

Project description

Geometry of Wasserstein spaces under study

The transport theory that was formalised by the French mathematician Gaspard Monge in 1781 explores the optimal transport and allocation of resources. The theory has since then found application in a number of fields, including mathematical physics and probability theory. Funded by the Marie Skłodowska-Curie Actions programme, the GWFP project will study the metric structure of classical Wasserstein spaces (which provide a metric on a space of probability measures), with a strong emphasis on the classification of distance-preserving maps.

Objective

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.

Coordinator

INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA
Net EU contribution
€ 186 167,04
Address
Am Campus 1
3400 Klosterneuburg
Austria

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Region
Ostösterreich Niederösterreich Wiener Umland/Nordteil
Activity type
Higher or Secondary Education Establishments
Links
Total cost
€ 186 167,04