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SUMMARY:Quantitative Stability\, Coercivity and Uniqueness of Optimal Tran
 sport Plans
DTSTART:20260930T083000Z
DTEND:20260930T100000Z
DTSTAMP:20261010T191100Z
UID:indico-event-17379@indico.math.cnrs.fr
DESCRIPTION:Speakers: William Ford (CMAP & LMO)\n\nWe prove three quantita
 tive results regarding optimal transport plans for the quadratic cost:\n 
 \n1. Bi-marginal quantitative stability: For probability measures on R^d s
 upported in fixed compact sets\, we prove that quadratic optimal transport
  plans are quantitatively stable in Wasserstein distance under perturbatio
 n of both marginal measures\, assuming that one of the initial measures sa
 tisfies an upper Ahlfors regularity condition with exponent strictly great
 er than d-1.2. Coercivity: Under the same Ahlfors assumption\, we prove th
 at any transport plan on the product space must be quantitatively close to
  the optimal plan\, if it has similar marginals and a similar transport co
 st to the optimal value.3. Quantitative Uniqueness: We prove a quantitativ
 e version of Brenier's theorem. The Wasserstein diameter of the set of opt
 imal plans is controlled by the Wasserstein distance of one marginal measu
 re to a regular measure for which uniqueness holds. In this way\, "almost 
 uniqueness'' of optimal plans is quantified by the source measure being "a
 lmost regular''.\n \n\nhttps://indico.math.cnrs.fr/event/17379/
LOCATION:112 (Braconnier)
URL:https://indico.math.cnrs.fr/event/17379/
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