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Consider the centered Gaussian field on the lattice $mathbb{Z}^d,$ $d$ large enough, with covariances given by the inverse of $sum_{j=k}^K q_j(-Delta)^j,$ where $Delta$ is the discrete Laplacian and $q_j in mathbb{R},kleq jleq K,$ the $q_j$ satisfying certain additional conditions. We extend a previously known result to show that the probability that all spins are nonnegative on a box of side-length $N$ has an exponential decay at rate of order $N^{d-2k}log{N}.$ The constant is given in terms of a higher-order capacity of the unit cube, analogous to the known case of the lattice free field. This result then allows us to show that, if we condition the field to stay positive in the $N-$box, the local sample mean of the field is pushed to a height of order $sqrt{log N}.$
We consider the real-valued centered Gaussian field on the four-dimensional integer lattice, whose covariance matrix is given by the Greens function of the discrete Bilaplacian. This is interpreted as a model for a semiflexible membrane. $d=4$ is the
We study the behaviour of the point process of critical points of isotropic stationary Gaussian fields. We compute the main term in the asymptotic expansion of the two-point correlation function near the diagonal. Our main result implies that for a g
We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not $g$-measures. The main ingredient in the proof is the occurrence of an entropic repulsi
In this paper we investigate the scaling limit of the range (the set of visited vertices) for a class of critical lattice models, starting from a single initial particle at the origin. We give conditions on the random sets and an associated ancestral
Let $r=r(n)$ be a sequence of integers such that $rleq n$ and let $X_1,ldots,X_{r+1}$ be independent random points distributed according to the Gaussian, the Beta or the spherical distribution on $mathbb{R}^n$. Limit theorems for the log-volume and t