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Virosztek Dániel (IST Austria): Isometries of Wasserstein spaces 



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 nonsurjective 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 nonsurjective 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 apriori nonsurjective 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 twoelement group C_2 for p>1. For the real line, we show that the pWasserstein 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 nonsurjective Wasserstein isometries on the ddimensional torus will also be shown. 
Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi vértanúk tere 1., Szeged 
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