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24 10 IM ProbabilitySeminar noticiaTitle: "Properties of the gradient squared of the Gaussian free field"
Speaker: Sergio I. López  (Universidad Nacional Autónoma de México)
Date: 30/10/2023
Time: 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time)
Local: Online

This meeting will take place on Google Meet, through the link HERE.

Abstract: In this talk we study the scaling limit of a random field which is a non-linear transformation of the gradient Gaussian free field. More precisely, our object of interest is the recentered square of the norm of the gradient Gaussian free field at every point of the square lattice. Surprisingly, in dimension 2 this field bears a very close connection to the 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 limiting 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 these results to higher dimensions as well.

Joint work with Rajat Subhra Hazra (Leiden), Alan Rapoport (Utrecht) and Wioletta Ruszel (Utrecht)

More complete information about the seminars can be found at HERE


Organizers: Giulio Iacobelli e Maria Eulalia Vares