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SUMMARY:Brownian excursions\, conformal loop ensembles and critical Liouvi
 lle quantum gravity - Ellen Powell (Durham)
DTSTART:20211130T140000Z
DTEND:20211130T150000Z
UID:TALK164479@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:In a groundbreaking work\, Duplantier\, Miller and Sheffield s
 howed that subcritical Liouville quantum gravity (LQG) coupled with Schram
 m-Loewner evolutions (SLE) can be described by the mating of two continuum
  random trees. In this talk I will discuss the counterpart of their result
  for critical LQG and SLE. More precisely\, I will explain how\, as we app
 roach criticality from the subcritical regime\, the space-filling SLE dege
 nerates to the uniform CLE_4 exploration introduced by Werner and Wu\, tog
 ether with a collection of independent coin tosses indexed by the branch p
 oints of the exploration. Furthermore\, although the pair of continuum ran
 dom trees collapse to a single continuum random tree in the limit we can a
 pply an appropriate affine transform to the encoding Brownian motions befo
 re taking the limit\, and get convergence to a Brownian half-plane excursi
 on. I will try to explain how observables of interest in the critical CLE 
 decorated LQG picture are encoded by a growth fragmentation naturally embe
 dded in the Brownian excursion. This talk is based on joint work with Juha
 n Aru\, Nina Holden and Xin Sun. 
LOCATION:MR12  Centre for Mathematical Sciences
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