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SUMMARY:Scaling limits of random planar maps with large faces - Gregory Mi
 ermont (Paris-Sud Orsay)
DTSTART:20100119T163000Z
DTEND:20100119T173000Z
UID:TALK22460@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:We discuss asymptotics of large random maps in which the distr
 ibution of the degree of a typical face has a polynomial tail. When the nu
 mber of vertices of the map goes to infinity\, the appropriately rescaled 
 distances from a base vertex can be described in terms of a new random pro
 cess\, defined in terms of a field of Brownian bridges over the so-called 
 stable trees. This allows to obtain weak convergence results in the Gromov
 -Hausdorff sense for these "maps with large faces"\, viewed as metric spac
 es by endowing the set of their vertices with the graph distance. The limi
 ting spaces form a one-parameter family of "stable maps"\, in a way parall
 el to the fact that the so-called Brownian map is the conjectured scaling 
 limit for families of maps with faces-degrees having exponential tails. Th
 is work takes part of its motivation from the study of statistical physics
  models on random maps. Joint work with J.-F. Le Gall. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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