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CATEGORIES:Probability
SUMMARY:Geodesic stars in Brownian geometry - Jean-Francoi
s Le Gall (Universite Paris-Saclay)
DTSTART;TZID=Europe/London:20211123T140000
DTEND;TZID=Europe/London:20211123T150000
UID:TALK164476AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/164476
DESCRIPTION:Planar maps\, which are finite connected graphs em
bedded in the sphere\, are basic discrete models o
f random geometry and are usually chosen uniformly
at random in a given class\, for instance the cla
ss of all triangulations with a fixed number of fa
ces. The so-called Brownian sphere\, or Brownian
map\, is the random metric space obtained as the u
niversal scaling limit of random planar maps equip
ped with the usual graph distance\, in the Gromov-
Hausdorff topology. We discuss geodesics in the Br
ownian sphere. It has been known for some time tha
t any two geodesics starting from a typical point
of the Brownian sphere must coincide near their st
arting point. However\, for any m < 5\, there are
exceptional points called geodesic stars with m ar
ms\, which are starting points of m disjoint geod
esics. We prove that the Hausdorff dimension of ge
odesic stars with m arms is equal to 5-m . This co
mplements an earlier work of Miller and Qian who p
roved that this Hausdorff dimension is bounded abo
ve by 5-m.\n\nThe talk will be held online using z
oom. The link will be distributed to the probabil
ity seminar list. If you are not on the list and
would like to attend the talk\, please email Perla
Sousi (ps422@cam.ac.uk) for the link.
LOCATION:Online (Zoom)
CONTACT:Jason Miller
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