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SUMMARY:Geodesic stars in Brownian geometry - Jean-Francois Le Gall (Unive
 rsite Paris-Saclay)
DTSTART:20211123T140000Z
DTEND:20211123T150000Z
UID:TALK164476@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:Planar maps\, which are finite connected graphs embedded in th
 e sphere\, are basic discrete models of random geometry and are usually ch
 osen uniformly at random in a given class\, for instance the class of all 
 triangulations with a fixed number of faces.  The so-called Brownian spher
 e\, or Brownian map\, is the random metric space obtained as the universal
  scaling limit of random planar maps equipped with the usual graph distanc
 e\, in the Gromov-Hausdorff topology. We discuss geodesics in the Brownian
  sphere. It has been known for some time that any two geodesics starting f
 rom a typical point of the Brownian sphere must coincide near their starti
 ng point. However\, for any m < 5\, there are exceptional points called ge
 odesic stars with m arms\, which are starting points of  m disjoint geodes
 ics. We prove that the Hausdorff dimension of geodesic stars with m arms i
 s equal to 5-m . This complements an earlier work of Miller and Qian who p
 roved that this Hausdorff dimension is bounded above by 5-m.\n\nThe talk w
 ill be held online using zoom.  The link will be distributed to the probab
 ility seminar list.  If you are not on the list and would like to attend t
 he talk\, please email Perla Sousi (ps422@cam.ac.uk) for the link.
LOCATION:Online (Zoom)
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