Related papers: Extremes of some Gaussian random interfaces

Although there is an extensive literature on the maxima of Gaussian processes, there are relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is to develop such a bound, while also allowing for many…

We show the equivalence between the three approximation schemes for self-interacting (1+1)-D scalar field theories. Based on rigorous results of [1, 2], we are able to prove that the Gaussian approximation is very precise for certain limits…

We consider the lattice version of the free field in two dimensions and study the fractal structure of the sets where the field is unusually high (or low). We then extend some of our computations to the case of the free field conditioned on…

We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and…

This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…

We show that the centered maximum of a sequence of log-correlated Gaussian fields in any dimension converges in distribution, under the assumption that the covariances of the fields converge in a suitable sense. We identify the limit as a…

We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate rigorously the first expansion terms for the Gilbert disk…

We use the Stein-Chen method to study the extremal behaviour of the problem of extremes for univariate and bivariate geometric laws. We obtain a rate for the convergence to the Gumbel distribution of the law of the maximum of i. i. d.…

We consider the gradient field model in $\left[ -N,N\right] ^{2}\cap \mathbb{Z}^{2}$ with a uniformly convex interaction potential. Naddaf-Spencer \cite{NS} and Miller \cite{Mi} proved that the macroscopic averages of linear statistics of…

Gibbsian structure in random point fields has been a classical tool for studying their spatial properties. However, exact Gibbs property is available only in a relatively limited class of models, and it does not adequately address many…

In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima.…

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…

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

We derive a scale-free bound on the density of the maximum of a centered Gaussian vector. The basic bound is non-uniform, depends logarithmically on the dimension, and allows any covariance matrix. When the largest marginal variance is…

The paper covers the design and analysis of experiments to discriminate between two Gaussian process models, such as those widely used in computer experiments, kriging, sensor location and machine learning. Two frameworks are considered.…

A Gaussian variational approximation is often used to study interfaces in random media. By considering the 1+1 dimensional directed polymer in a random medium, it is shown here that the variational Ansatz typically leads to a negative…

We introduce a framework to derive quantitative central limit theorems in the context of non-linear approximation of Gaussian random variables taking values in a separable Hilbert space. In particular, our method provides an alternative to…

We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…

Massive and massless Gaussian free fields can be described as generalized Gaussian processes indexed by an appropriate space of functions. In this article we study various approaches to approximate these fields and look at the fractal…

This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on…