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DTSTAMP:20260406T032703Z
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\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Daniel Virosztek: The isometry group of Wasserstein spaces: the Hil
 bertian case
URL:https://talks-calendar.ista.ac.at/events/2887
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