Related papers: The Curvature Effect in Gaussian Random Fields
Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the…
We present a systematic study of one-loop quantum corrections in scalar effective field theories from a geometric viewpoint, emphasizing the role of field-space curvature and its renormalisation. By treating the scalar fields as coordinates…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by…
In this paper, we consider a classic problem concerning the high excursion probabilities of a Gaussian random field $f$ living on a compact set $T$. We develop efficient computational methods for the tail probabilities $P(\sup_T f(t) > b)$…
The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the…
Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian,…
The statistical translation invariance of cosmological random fields is broken by a finite survey boundary, correlating the observable Fourier modes. Standard methods for generating Gaussian fields either neglect these correlations, or are…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
Macroscopic fields like electromagnetic, MHD, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete…
When the equations that govern the dynamics of a random field are nonlinear, the field can develop with time non-Gaussian statistics even if its initial condition is Gaussian. Here, we provide a general framework for calculating the effect…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
Level curvature is a measure of sensitivity of energy levels of a disordered/chaotic system to perturbations. In the bulk of the spectrum Random Matrix Theory predicts the probability distributions of level curvatures to be given by…
We study the sample paths properties of Operator scaling Gaussian random fields. Such fields are anisotropic generalizations of anisotropic self-similar random fields as anisotropic Fractional Brownian Motion. Some characteristic properties…
Gaussian random fields are a powerful tool for modeling environmental processes. For high dimensional samples, classical approaches for estimating the covariance parameters require highly challenging and massive computations, such as the…
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…
In this Letter, we use a model fluid mechanics experiment to elucidate the impact of curvature heterogeneities on two-dimensional fields deriving from harmonic potential functions. This result is directly relevant to explain the smooth…
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…
Gaussian process (GP) emulator has been used as a surrogate model for predicting force field and molecular potential, to overcome the computational bottleneck of molecular dynamics simulation. Integrating both atomic force and energy in…