Large deviation results for percolation of Gaussian Free Field level-sets
Franco Severo (IHES)

We consider the Gaussian Free Field (GFF) on $\mathbb\{Z\}^d$, for $d geq 3$, and its level-sets above a given height $h\\in \\mathbb\{R\}$. As $h$ varies, this defines a natural percolation model with slow decay of correlations. This model, first studied in the 80s by Bricmont, Lebowitz and Maes, became a subject of intense research over the last decade due to developments on renormalization theory. In this talk we shall discuss some of these developments, with special emphasis on large deviation results for percolation events. We will explain how the so called "entropic repulsion phenomenon", first observed by Bolthausen, Deuschel and Zeitouni, allows one to prove large deviation results for the GFF level-sets which are not even available for independent percolation. This exemplifies how more correlations sometimes can make things more treatable.
[Based on joint works with S. Goswami, A. Prévost and P-F. Rodriguez]