This book is concerned with extreme value theory for stochastic processes whose finite-
dimensional distributions are heavy-tailed in the restrictive sense of regular variation. These …

We study the local structure of the extremal process associated with the Discrete Gaussian
Free Field (DGFF) in scaled-up (square-) lattice versions of bounded open planar domains …

These lecture notes offer a gentle introduction to the two-dimensional Discrete Gaussian
Free Field with particular attention paid to the scaling limits of the level sets at heights …

We show that the centred maximum of the four-dimensional membrane model on a box of
sidelength N converges in distribution. To do so, we use a criterion of Ding, Roy and …

On the integer lattice, we consider the discrete membrane model, a random interface in
which the field has Laplacian interaction. We prove that, under appropriate rescaling, the …

The Discrete Gaussian Chain is a model of interfaces $\Psi:\mathbf {Z}\to\mathbf {Z} $
governed by the Hamiltonian $$ H (\Psi)=\sum_ {i\neq j} J_\alpha (| ij|)|\Psi_i-\Psi_j|^ 2 …

We consider the Gaussian interface model in the presence of random external fields, that is
the finite volume (random) Gibbs measure on R Λ N, Λ N=[-N, N] d∩ Z d with Hamiltonian …

We characterize the behavior of a random discrete interface ϕ on [− L, L] d∩ Z d with
energy∑ V (Δ ϕ (x)) as L→∞, where Δ is the discrete Laplacian and V is a uniformly convex …

We consider level-set percolation for the Gaussian membrane model on Z d, with d≥ 5, and
establish that as h∈ R varies, a non-trivial percolation phase transition for the level-set …

Cette thèse porte sur le phénomène de superconcentration qui apparaît dans l'étude des
fluctuations de divers modèles de la recherche actuelle (matrices aléatoires, verres de …