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SUMMARY:Spectral gap properties for random walks on homogeneous spaces: ex
 amples and consequences - Guivarch\, Y (Universit de Rennes 1)
DTSTART:20140704T103000Z
DTEND:20140704T112000Z
UID:TALK53316@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: J.-P Conze\, B. Bekka\, E .LePage\n\n Let E be a h
 omogeneous space of a Lie group G\, p a finitely supported probability mea
 sure on G\, such that supp(p) generates topologically G. We show that\, in
  various situations\, convolution by p has a spectral gap on some suitable
  functional space on E . We consider in particular Hilbert spaces and Hold
 er spaces on E and actions by affine transformations. If G is the motion g
 roup of Euclidean space V \,we get equidistribution of the random walk on 
 V. If G is the affine group of V\,p has a stationary probability\, and the
  projection of p on GL(V) satisfies "generic" conditions we get that the r
 andom walk satisfies Frechet's extreme law \, and Sullivan's Logarithm law
 .\n
LOCATION:Seminar Room 1\, Newton Institute
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