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SUMMARY:Behaviour near the extinction time in stable fragmentation process
 es - Christina Goldschmidt (Oxford)
DTSTART:20080506T130000Z
DTEND:20080506T140000Z
UID:TALK11794@talks.cam.ac.uk
CONTACT:Norros I.
DESCRIPTION:The stable fragmentations are particularly nice examples of th
 e self-similar fragmentation processes introduced by Bertoin. They are der
 ived by looking at the masses of the subtrees formed by discarding the the
  parts of a stable continuum random tree below height t\, for t greater th
 an or equal to 0. Such a fragmentation possesses a parameter alpha which l
 ies between -1/2 and 0\, called the index of self-similarity\; heuristical
 ly\, any block of mass m splits at a rate proportional to m^{alpha}. Since
  alpha is negative\, this means that smaller blocks split faster than larg
 er ones. Indeed\, small blocks split faster and faster until they are redu
 ced to dust (blocks of size 0). The whole state is entirely reduced to dus
 t in some almost surely finite time zeta\, called the extinction time. We 
 give a detailed limiting description of the distribution of a stable fragm
 entation of index alpha as it approaches its extinction time. \n\nThis is 
 work in progress with Benedicte Haas of Universite Paris-Dauphine. \n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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