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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Random Planar Maps 4 - Miermont\, G (ENS - Lyon)
DTSTART;TZID=Europe/London:20150115T160000
DTEND;TZID=Europe/London:20150115T170000
UID:TALK57086AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/57086
DESCRIPTION:A map is a gluing of a finite number of polygons\,
forming a connected orientable topological surfac
e. It can be interpreted as assigning this surface
a discrete geometry\, and the theoretical physics
literature in the 80-90s argued that random maps
are an appropriate discrete model for the theory o
f 2-dimensional quantum gravity\, which involves i
ll-defined integrals over all metrics on a given s
urface. The idea is to replace these integrals by
finite sums\, for instance over all triangulation
of the sphere with a large number of faces\, hopin
g that such triangulations approximate a limiting
continuum random surface. \n\nIn the recent years\
, much progress has been made in the mathematical
understanding of the latter problem. In particular
\, it is now known that many natural models of ran
dom planar maps\, for which the faces degrees rema
in small\, admit a universal scaling limit\, the B
rownian map. \n\nOther models\, favorizing large f
aces\, also admit a one-parameter family of scalin
g limits\, called stable maps. The latter are beli
eved to describe the asymptotic geometry of random
maps carrying statistical physics models\, as has
now been established in some important cases (inc
luding the so-called rigid O(n) model on quadrangu
lations). \n\nThis mini-course will review the mai
n aspects of these themes.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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