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CATEGORIES:Probability
SUMMARY:Scaling limits of random planar maps with large fa
 ces - Gregory Miermont (Paris-Sud Orsay)
DTSTART;TZID=Europe/London:20100119T163000
DTEND;TZID=Europe/London:20100119T173000
UID:TALK22460AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/22460
DESCRIPTION:We discuss asymptotics of large random maps in whi
 ch the distribution of the degree of a typical fac
 e has a polynomial tail. When the number of vertic
 es of the map goes to infinity\, the appropriately
  rescaled distances from a base vertex can be desc
 ribed in terms of a new random process\, defined i
 n terms of a field of Brownian bridges over the so
 -called stable trees. This allows to obtain weak c
 onvergence results in the Gromov-Hausdorff sense f
 or these "maps with large faces"\, viewed as metri
 c spaces by endowing the set of their vertices wit
 h the graph distance. The limiting spaces form a o
 ne-parameter family of "stable maps"\, in a way pa
 rallel to the fact that the so-called Brownian map
  is the conjectured scaling limit for families of 
 maps with faces-degrees having exponential tails. 
 This work takes part of its motivation from the st
 udy of statistical physics models on random maps. 
 Joint work with J.-F. Le Gall. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
 B
CONTACT:Berestycki
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