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SUMMARY:Maximal couplings and geometry - Dr Sayan Banerjee\, University of
  Warwick
DTSTART:20141111T163000Z
DTEND:20141111T173000Z
UID:TALK55906@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:Maximal couplings are couplings of Markov processes where the 
 tail probabilities of the coupling time attain the total variation lower b
 ound (Aldous bound) uniformly for all time. Markovian couplings are coupli
 ng strategies where neither process is allowed\nto look into the future of
  the other before making the next transition. These are easier to describe
  and play a fundamental role in many branches of probability and analysis.
  Hsu and Sturm proved that the reflection coupling of Brownian motion is t
 he\nunique Markovian maximal coupling (MMC) of Brownian motions starting f
 rom two different points. Later\, Kuwada proved that to have a MMC for Br
 ownian motions\non a Riemannian manifold\, the manifold should have a refl
 ection structure\, and thus proved the first result connecting a purely p
 robabilistic phenomenon (MMC) to the geometry of the underlying space.\nIn
  this work\, we investigate general elliptic diffusions on Riemannian mani
 folds\, and show how the geometry (dimension of the isometry group and \nf
 lows of isometries) plays a fundamental role in classifying the space and 
 the generator of the diffusion for which an MMC exists. We also describe t
 hese diffusions in terms of Killing vector fields\n(generators of rigid 
 motions on manifolds) and dilation vector elds around a point.\n\nThis is
  joint work with W.S. Kendall.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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