Related papers: Almost Sure Uniform Convergence of a Random Gaussi…
Completing the study initiated by Mounaix and Collet [J. Stat. Phys. {\bf 143}, 139-147 (2011)], we investigate the realizations of a Gaussian random field in the limit where a given (general) quadratic form of the field is large.…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…
We present a self-contained proof of a uniform bound on multi-point correlations of trigonometric functions of a class of Gaussian random fields. It corresponds to a special case of the general situation considered in [Hairer-Xu], but with…
We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…
Let $\mathcal{T}$ be a rooted tree endowed with the natural partial order $\preceq$. Let $(Z(v))_{v\in \mathcal{T}}$ be a sequence of independent standard Gaussian random variables and let $\alpha = (\alpha_k)_{k=1}^\infty$ be a sequence of…
We prove that under fairly general conditions properly rescaled determinantal random point field converges to a generalized Gaussian random process.
We investigate the sub-Gaussian property for almost surely bounded random variables. If sub-Gaussianity per se is de facto ensured by the bounded support of said random variables, then exciting research avenues remain open. Among these…
Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our…
We obtain an almost sure limit theorem for the maximum of nonstationary random fields under some dependence conditions.
In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems…
We investigate the conditional distributions of two Banach space valued, jointly Gaussian random variables. In particular, we show that these conditional distributions are again Gaussian and that their means and covariances can be…
This article gives a new proof that fully connected neural networks with random weights and biases converge to Gaussian processes in the regime where the input dimension, output dimension, and depth are kept fixed, while the hidden layer…
This is the first in a series of two works which study the discrete Gaussian free field on the binary tree when all leaves are conditioned to be positive. In this work, we obtain sharp asymptotics for the probability of this "hard-wall…
We study the problem of a random Gaussian vector field given that a particular real quadratic form $\mathcal{Q}$ is arbitrarily large. We prove that in such a case the Gaussian field is primarily governed by the fundamental eigenmode of a…
The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the corresponding additive functionals have same distributions…
Fine regularity of stochastic processes is usually measured in a local way by local H\"older exponents and in a global way by fractal dimensions. Following a previous work of Adler, we connect these two concepts for multiparameter Gaussian…
This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…