We consider upper level sets of the Gaussian free field (GFF) on Z d, for d≥ 3, above a
given real-valued height parameter h. As h varies, this defines a canonical percolation …

We establish the sharpness of the phase transition for a wide class of Gaussian percolation
models, on Z d or R d, d≥ 2, with correlations decaying at least algebraically with exponent …

We prove that the connectivity of the level sets of a wide class of smooth centred planar
Gaussian fields exhibits a phase transition at the zero level that is analogous to the phase …

We develop techniques to study the phase transition for planar Gaussian percolation models
that are not (necessarily) positively correlated. These models lack the property of positive …

We consider the level-sets of continuous Gaussian fields on R d above a certain level− l∈
R, which defines a percolation model as l varies. We assume that the covariance kernel …

For the Bargmann–Fock field on R d with d≥ 3, we prove that the critical level ℓ c (d) of the
percolation model formed by the excursion sets {f≥ ℓ} is strictly positive. This implies that for …

Many complex statistical mechanical models have intricate energy landscapes. The ground
state, or lowest energy state, lies at the base of the deepest valley. In examples such as spin …

We prove a general Russo–Seymour–Welsh (RSW) result valid for any invariant bond
percolation measure on Z 2 satisfying positive association. This means that the crossing …

In this article, we study the excursion sets 𝒟 p= f-1 ([-p,+∞[) where f is a natural real-analytic
planar Gaussian field called the Bargmann–Fock field. More precisely, f is the centered …

We study the decay of connectivity of the subcritical excursion sets of a class of strongly
correlated Gaussian fields. Our main result shows that, for smooth isotropic Gaussian fields …