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SUMMARY:A new approach to the Brownian web - Nathanael Berestycki (Cambrid
 ge)
DTSTART:20121127T163000Z
DTEND:20121127T173000Z
UID:TALK41768@talks.cam.ac.uk
CONTACT:12974
DESCRIPTION:The Brownian web was introduced by Arratia (1979) and Toth--We
 rner\n(1997)\, and corresponds informally to starting coalescing Brownian\
 nmotions from every space-time point in 1+1 dimensions. Inspired by the\nw
 ork of Schramm and Smirnov on the scaling limit of critical\npercolation\,
  we provide a new state space and topology for this\nprocess. In particula
 r\, this allows us to derive an invariance\nprinciple for coalescing rando
 m walks under an optimal second moment\ncondition on the increments of the
  underlying random walk. This stands\nin contrast with a series of previou
 s papers working under a different\ntopology\, where it was shown that exi
 stence of third moments was both\nnecessary and sufficient for this conver
 gence to hold. Our approach is\nsufficiently simple and general that we ca
 n handle substantially more\ncomplicated coalescing flows with little extr
 a work. For instance\nsimilar results are obtained in the case of coalesci
 ng Brownian\nmotions on recurrent fractals such as the Sierpinsky gasket. 
 This is\nthe first such result where the limiting paths do not enjoy the\n
 non-crossing property.\n\nJoint work with Christophe Garban (ENS Lyon) and
  Arnab Sen (Minnesota).\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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