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SUMMARY:Distances on the CLE(4)\, critical Liouville quantum gravity and 3
 /2-stable maps - Emmanuel Kammerer (Ecole Polytechnique)
DTSTART:20240206T153000Z
DTEND:20240206T163000Z
UID:TALK211486@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:Random planar maps with high degrees are expected to have scal
 ing limits related to the conformal loop ensemble (CLE) equipped with an i
 ndependent Liouville quantum gravity (LQG). In the dilute case\, where inf
 ormally the degrees have finite expectations\, Bertoin\, Budd\, Curien and
  Kortchemski established the scaling limit of the distances to the root. H
 owever\, the scaling limit does not have an interpretation as a distance f
 rom the loops to the boundary in terms of LQG. I will focus on the critica
 l case where the probability that a vertex has degree k is of order k^-2. 
 In this case\, the distances from the root to the high degree vertices sat
 isfy a scaling limit\, and this scaling limit is related to a quantum dist
 ance to the boundary on a CLE(4)-decorated critical LQG introduced by Aru\
 , Holden\, Powell and Sun. Finally\, I will draw a connection with a confo
 rmally invariant distance to the boundary on the CLE(4) from Werner and Wu
 .
LOCATION:MR12
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