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SUMMARY:Geodesics in Brownian surfaces - Bettinelli\, J (Universit de Lorr
 aine)
DTSTART:20150129T100000Z
DTEND:20150129T110000Z
UID:TALK57589@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this talk\, we introduce a class of random metric spaces ca
 lled Brownian surfaces\, which generalize the famous Brownian map to the c
 ase of topologies more complicated than that of the sphere. More precisely
 \, these random surfaces arise as the scaling limit of random maps on a gi
 ven surface with a boundary. We will review the known results about these 
 rather wild random metric spaces and we will particularly focus on the geo
 desics starting from a uniformly chosen random point. This allow to charac
 terize some subsets of interest in terms of geodesics and\, in particular\
 , in terms of pairs of geodesics aiming at the same point and whose concat
 enation forms a loop not homotopic to 0.\n \nOur results generalize in par
 ticular the properties shown by Le Gall on geodesics in the Brownian map\,
  although our approach is completely different.\n
LOCATION:Seminar Room 1\, Newton Institute
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