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SUMMARY:On the geometry of discrete and continuous random planar maps - Le
  Gall\, J-F (Universit Paris-Sud 11)
DTSTART:20150422T080000Z
DTEND:20150422T090000Z
UID:TALK59154@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Co-author: Curien\, Nicolas (Universit Paris-Sud) \n\nWe discu
 ss 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-volume version of the Brownian map a
 nd is conjectured to be the universal scaling limit of many discrete rando
 m lattices such as the UIPT (uniform infinite planar triangulation) or the
  UIPQ (uniform infinite planar quadrangulation). The hull of radius r in t
 he Brownian plane is obtained by filling in the holes in the ball of radiu
 s r centered at the distinguished point. We obtain a complete description 
 of the process of hull volumes\, as well as several explicit formulas for 
 related distributions. In the discrete setting of the UIPT or the UIPQ\, w
 e derive similar results via a detailed study of the peeling process alrea
 dy inverstigated by Angel. We also apply our results to first-passage perc
 olation on these infinite random lattices. This is a joint work with Nicol
 as Curien.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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