We provide an existence theory for gradient Gibbs measures for Z-valued spin models on
regular trees which are not invariant under translations of the tree, assuming only …

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 …

We study how the typical gradient and typical height of a random surface are modified by the
addition of quenched disorder in the form of a random independent external field. The …

This thesis is concerned with Gibbs measures and gradient Gibbs measures for height
configurations on the regular tree with spatially homogeneous interaction of gradient type …

We prove estimates for the Green's function of the discrete bilaplacian in squares and cubes
in two and three dimensions which are optimal except possibly near the corners of the …

The seminal 1975 work of Brascamp-Lieb-Lebowitz initiated the rigorous study of Ginzberg-
Landau random surface models. It was conjectured therein that fluctuations are localized on …

Central limit theorems for linear statistics of lattice random fields (including spin models) are
usually proven under suitable mixing conditions or quasi-associativity. Many interesting …

In this article we study the scaling limit of the interface model on\, Z\,^ d Z d where the
Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any …

The discrete membrane model is a Gaussian random interface whose inverse covariance is
given by the discrete biharmonic operator on a graph. In literature almost all works have …

The membrane model is a Gaussian interface model with a Hamiltonian involving second
derivatives of the interface height. We consider the model in dimension d≥ 4 under the …