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SUMMARY:Properties of the gradient squared of the Gaussian free field - Al
 essandra Cipriani (UCL)
DTSTART:20230307T140000Z
DTEND:20230307T150000Z
UID:TALK198004@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:In this talk we study the scaling limit of a random field whic
 h is a non-linear transformation of the gradient Gaussian free field. More
  precisely\, our object of interest is the recentered square of the norm o
 f the gradient Gaussian free field at every point of the square lattice. S
 urprisingly\, in dimension 2 this field bears a very close connection to t
 he height-one field of the Abelian sandpile model studied in Dürre (2009)
 . In fact\, with different methods we are able to obtain the same scaling 
 limits of the height-one field: on the one hand\, we show that the limitin
 g cumulants are identical (up to a sign change) with the same conformally 
 covariant property\, and on the other that the same central limit theorem 
 holds when we view the interface as a random distribution. We generalize t
 hese results to higher dimensions as well.\njww Rajat Subhra Hazra (Leiden
 )\, Alan Rapoport (Utrecht) and Wioletta Ruszel (Utrecht)
LOCATION:MR12\, Centre for Mathematical Sciences
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