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DTSTAMP:20201021T163306Z
UID:1603377000@ist.ac.at
DTSTART:20201022T163000
DTEND:20201022T173000
DESCRIPTION:Speaker: Daniel Virosztek\nhosted by Laszlo Erdös\nAbstract: I
will report on the most recent step of our systematic study of Wasserstei
n isometries\, which is joint work with Gyorgy Pal Geher (U Reading) and T
amas Titkos (Renyi Inst.\, Budapest). Now we consider Wasserstein spaces o
ver a separable real Hilbert space H and describe the isometries for every
positive finite parameter p. The quadratic case (p=2) turns out to be an
infinite-dimensional analogon of Kloeckner's result on the isometries of
W_2(R^n) from 2010\, which says that W_2(R^n) admits non-trivial isometrie
s as well as trivial ones (which are governed by isometries of the underly
ing space). For p≠2\, we use a two-step argument. First\, we give a metr
ic characterization of Dirac masses and deduce that they are invariant und
er Wasserstein isometries (modulo trivial isometries). This metric charact
erization is essentially different for concave cost (p<1) and for convex
cost (p>=1). Then we introduce a quantity which we call the Wasserstein p
otential of a measure and which is invariant under Wasserstein isometries.
We show that the potential function completely determines the measure for
every non-even positive p\, and hence we deduce isometric rigidity\, whic
h means that Isom(W_p(H))=Isom(H). For p=4\,6\,8\,... we prove isometric r
igidity\, although in this case\, the Wasserstein potential does not carry
enough information to recover the measure.If time allows\, I will demonst
rate the efficiency of the potential function method on different underlyi
ng spaces (including spheres\, tori\, and projective planes) as well.
LOCATION:online via Zoom\, IST Austria
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:The isometry group of Wasserstein spaces: the Hilbertian case
URL:https://talks-calendar.app.ist.ac.at/events/2887
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