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UID:20250712T202302EDT-9446r4gJej@132.216.98.100
DTSTAMP:20250713T002302Z
DESCRIPTION:Title: Area measures and branched polymers in supercritical Lio
 uville quantum gravity.\n\nAbstract: Liouville quantum gravity (LQG) is a 
 'canonical' one-parameter model of surfaces with random geometry\, where t
 he parameter c >1 is the central charge of the associated conformal field 
 theory. Compared to the subcritical and critical phases with c ≥ 25 (corre
 sponding to 𝛾 ≤ 2)\, much less is known about the geometry of LQG in the s
 upercritical phase c ∈ (1\,25). Recent work of Ding and Gwynne has shown h
 ow to construct LQG in this phase as a planar random geometry associated w
 ith the Gaussian free field\, which exhibits 'infinite spikes.' In contras
 t\, a number of results from physics\, dating back to the 1980s\, suggest 
 that supercritical LQG surfaces should look like the continuum random tree
 .\n\nIn this talk\, I will give a result that reconciles these two descrip
 tions. More precisely\, for a family of random planar maps in the universa
 lity class of supercritical LQG\, if we condition on the (small probabilit
 y) event that the planar map is finite\, then the scaling limit is the con
 tinuum random tree. Separately\, we show that there does not exist any loc
 ally finite measure associated with supercritical LQG which is locally det
 ermined by the field and satisfies the LQG coordinate change formula. Both
  results are based on a branching process description of supercritical LQG
  which comes from its coupling with CLE_4 by Ang and Gwynne.\n\nThis is jo
 int work with Manan Bhatia and Ewain Gwynne.\n\n \n
DTSTART:20241128T163000Z
DTEND:20241128T173000Z
LOCATION:Room 719A\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Jinwoo Sung (University of Chicago)
URL:/mathstat/channels/event/jinwoo-sung-university-ch
 icago-361376
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