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CATEGORIES:Probability
SUMMARY:Brownian excursions\, conformal loop ensembles and
critical Liouville quantum gravity - Ellen Powell
(Durham)
DTSTART;TZID=Europe/London:20211130T140000
DTEND;TZID=Europe/London:20211130T150000
UID:TALK164479AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/164479
DESCRIPTION:In a groundbreaking work\, Duplantier\, Miller and
Sheffield showed that subcritical Liouville quant
um gravity (LQG) coupled with Schramm-Loewner evol
utions (SLE) can be described by the mating of two
continuum random trees. In this talk I will discu
ss the counterpart of their result for critical LQ
G and SLE. More precisely\, I will explain how\, a
s we approach criticality from the subcritical reg
ime\, the space-filling SLE degenerates to the uni
form CLE_4 exploration introduced by Werner and Wu
\, together with a collection of independent coin
tosses indexed by the branch points of the explora
tion. Furthermore\, although the pair of continuum
random trees collapse to a single continuum rando
m tree in the limit we can apply an appropriate af
fine transform to the encoding Brownian motions be
fore taking the limit\, and get convergence to a B
rownian half-plane excursion. I will try to explai
n how observables of interest in the critical CLE
decorated LQG picture are encoded by a growth frag
mentation naturally embedded in the Brownian excur
sion. This talk is based on joint work with Juhan
Aru\, Nina Holden and Xin Sun.
LOCATION:MR12 Centre for Mathematical Sciences
CONTACT:Jason Miller
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