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SUMMARY:Random Planar Maps 3 - Miermont\, G (ENS - Lyon)
DTSTART:20150114T090000Z
DTEND:20150114T100000Z
UID:TALK57019@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A map is a gluing of a finite number of polygons\, forming a c
 onnected orientable topological surface. It can be interpreted as assignin
 g this surface a discrete geometry\, and the theoretical physics literatur
 e in the 80-90s argued that random maps are an appropriate discrete model 
 for the theory of 2-dimensional quantum gravity\, which involves ill-defin
 ed integrals over all metrics on a given surface. The idea is to replace t
 hese integrals by finite sums\, for instance over all triangulation of the
  sphere with a large number of faces\, hoping that such triangulations app
 roximate a limiting continuum random surface. \n\nIn the recent years\, mu
 ch progress has been made in the mathematical understanding of the latter 
 problem. In particular\, it is now known that many natural models of rando
 m planar maps\, for which the faces degrees remain small\, admit a univers
 al scaling limit\, the Brownian map. \n\nOther models\, favorizing large f
 aces\, also admit a one-parameter family of scaling limits\, called stable
  maps. The latter are believed to describe the asymptotic geometry of rand
 om maps carrying statistical physics models\, as has now been established 
 in some important cases (including the so-called rigid O(n) model on quadr
 angulations). \n\nThis mini-course will review the main aspects of these t
 hemes.\n
LOCATION:Seminar Room 1\, Newton Institute
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