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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Rothschild Distinguished Visiting Fellow Lecture:
Random maps and random 2-dimensional geometries -
Miermont\, G (ENS - Lyon)
DTSTART;TZID=Europe/London:20150202T160000
DTEND;TZID=Europe/London:20150202T170000
UID:TALK57681AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/57681
DESCRIPTION:A map is a graph embedded into a 2-dimensional sur
face\, considered up to homeomorphisms. In a way\,
such an object endows the surface with a discrete
metric\, so that a map taken at random is a natur
al candidate for a notion of "discrete random metr
ic surface". More precisely\, it is expected (and
proved in an evergrowing number of cases) that upo
n re-scaling the distances in an appropriate fashi
on\, a large random map converges to a random metr
ic space that is homeomorphic to the surface one s
tarted with. \n\nThis is reminiscent of the well-k
nown convergence of random walks to Brownian motio
n. Similarly to the latter\, the random continuum
objects that appear as scaling limits of random ma
ps are very irregular spaces\, by no means close t
o being smooth Riemannian manifolds. This makes t
heir study even more interinsting\, since it is ne
cessary to find the geometric notions that still m
ake sense in this context\, like geodesic paths. \
n\nBy contrast with these "continuous" notions\, w
e will see that the study of scaling limits of ran
dom maps relies strongly on tools of a purely comb
inatorial nature. We will also discuss conjectures
which\, quite surprisingly\, connect these scalin
g limits with conformally invariant random fields
in the plane. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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