This work is concerned with fractional Gaussian fields, ie Gaussian fields whose covariance
operator is given by the inverse fractional Laplacian $(-\Delta)^{-s} $(where, in particular, we …

In this article, we study stochastic homogenization of non-homogeneous Gaussian free
fields Ξ g, a and bi-Laplacian fields Ξ b, a. They can be characterized as follows: for f= δ the …

For an arbitrary dimension nn, we study: the polyharmonic Gaussian field h L h_L on the
discrete torus TL n= 1 LZ n/Z n T^n_L=1LZ^n/Z^n, that is the random field whose law on RTL …

Abstract In Cipriani et al.(2017), the authors proved that, with the appropriate rescaling, the
odometer of the (nearest neighbours) divisible sandpile on the unit torus converges to a bi …

The divisible sandpile model is a fixed-energy continuous counterpart of the Abelian
sandpile model. We start with a random initial configuration and redistribute mass …

In chapter 2 we investigate the behavior around the fixed-energy sandpile's phase transition
as conjectured in [9]. In the course of our investigations we define a supercritical threshold …