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UID:0viuig2vrh7mi5rkrpfsplbsl0@google.com
CATEGORIES:{lang hu}Analízis szeminárium{/lang}{lang en}Analysis seminar{/lang}
SUMMARY:Virosztek Dániel (IST Austria): Isometries of Wasserstein spaces
LOCATION:Bolyai Intézet, I. emelet, Riesz terem, Aradi vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE: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-surjectiv
e isometries of Wasserstein spaces over the countable discrete metric space
and the unit interval, as well as the structure of surjective isometries o
f Wasserstein spaces over the real line.
It turned out that non-surject
ive Wasserstein isometries over the discrete metric space form a large fami
ly and can be described by a special kind of N x(0,1]-indexed family of non
negative finite measures.
For the unit interval, we obtain that the a-p
riori non-surjective isometries are actually surjective, and the isometry g
roup 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-Wasse
rstein space is isometrically rigid --- that is, its isometry group coincid
es with that of the real line --- if and only if p is not equal to 2. A pro
mising approach to characterize non-surjective Wasserstein isometries on th
e d-dimensional torus will also be shown.
DTSTAMP:20240329T065232Z
DTSTART;TZID=Europe/Budapest:20190924T100000
DTEND;TZID=Europe/Budapest:20190924T110000
SEQUENCE:0
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