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CATEGORIES:Probability
SUMMARY:Properties of the gradient squared of the Gaussian
free field - Alessandra Cipriani (UCL)
DTSTART;TZID=Europe/London:20230307T140000
DTEND;TZID=Europe/London:20230307T150000
UID:TALK198004AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198004
DESCRIPTION:In this talk we study the scaling limit of a rando
m field which is a non-linear transformation of th
e gradient Gaussian free field. More precisely\, o
ur object of interest is the recentered square of
the norm of the gradient Gaussian free field at ev
ery point of the square lattice. Surprisingly\, in
dimension 2 this field bears a very close connect
ion to the height-one field of the Abelian sandpil
e model studied in DÃ¼rre (2009). In fact\, with di
fferent methods we are able to obtain the same sca
ling limits of the height-one field: on the one ha
nd\, we show that the limiting cumulants are ident
ical (up to a sign change) with the same conformal
ly covariant property\, and on the other that the
same central limit theorem holds when we view the
interface as a random distribution. We generalize
these results to higher dimensions as well.\njww R
ajat Subhra Hazra (Leiden)\, Alan Rapoport (Utrech
t) and Wioletta Ruszel (Utrecht)
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Perla Sousi
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