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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the geometry of discrete and continuous random
planar maps - Le Gall\, J-F (Universit Paris-Sud 1
1)
DTSTART;TZID=Europe/London:20150422T090000
DTEND;TZID=Europe/London:20150422T100000
UID:TALK59059AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/59059
DESCRIPTION:Co-author: Curien\, Nicolas (Universit Paris-Sud)
\n\nWe discuss some recent results concerning the
geometry of discrete and continuous random planar
maps. In the continuous setting\, we consider the
so-called Brownian plane\, which is an infinite-vo
lume version of the Brownian map and is conjecture
d to be the universal scaling limit of many discre
te random lattices such as the UIPT (uniform infin
ite planar triangulation) or the UIPQ (uniform inf
inite planar quadrangulation). The hull of radius
r in the Brownian plane is obtained by filling in
the holes in the ball of radius r centered at the
distinguished point. We obtain a complete descript
ion of the process of hull volumes\, as well as se
veral explicit formulas for related distributions.
In the discrete setting of the UIPT or the UIPQ\,
we derive similar results via a detailed study of
the peeling process already inverstigated by Ange
l. We also apply our results to first-passage perc
olation on these infinite random lattices. This is
a joint work with Nicolas Curien.\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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