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Virosztek Dániel (IST Austria): Isometries of Wasserstein spaces

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Tuesday, 24. September 2019, 10:00 - 11:00
I will report on our study of Wasserstein isometries --- a joint work with György Pál Gehér (University of Reading) and Tamás Titkos (Rényi Institute, Budapest). More precisely, I will present the description of non-surjective isometries of Wasserstein spaces over the countable discrete metric space and the unit interval, as well as the structure of surjective isometries of Wasserstein spaces over the real line.
It turned out that non-surjective Wasserstein isometries over the discrete metric space form a large family and can be described by a special kind of N x(0,1]-indexed family of nonnegative finite measures.
For the unit interval, we obtain that the a-priori non-surjective isometries are actually surjective, and the isometry group of the Wasserstein space is the Klein group C_2 x C_2 for p=1, and the two-element group C_2 for p>1. For the real line, we show that the p-Wasserstein space is isometrically rigid --- that is, its isometry group coincides with that of the real line --- if and only if p is not equal to 2. A promising approach to characterize non-surjective Wasserstein isometries on the d-dimensional torus will also be shown.
Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi vértanúk tere 1., Szeged


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