Séminaire de Probabilités commun ICJ/UMPA

A characterisation of the Gaussian free field

by Nathanael Berestycki

Fokko du Cloux (Bâtiment Braconnier, La Doua)

Fokko du Cloux

Bâtiment Braconnier, La Doua

The planar Gaussian free field arises as a universal scaling limit for a broad range of models from statistical physics. In this work we prove that any random distribution satisfying conformal invariance, a form of domain Markov property and a fourth moment condition must be a multiple of the Gaussian free field. We will also discuss several open problems concerning the situation beyond the Gaussian case.

Joint work with Ellen Powell (ETH) and Gourab Ray (Victoria).