Related papers: The Curvature Effect in Gaussian Random Fields
In this article we study two related models of quantum geometry: generic random trees and two-dimensional causal triangulations. The Hausdorff and spectral dimensions that arise in these models are calculated and their relationship with the…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
Geometrical random multiplicative cascade processes are often used to model positive-valued multifractal fields such as for example the energy dissipation field of fully developed turbulence. A dynamical generalisation of these models is…
Fast Fourier transforms are used to develop algorithms for the fast generation of correlated Gaussian random fields on d-dimensional rectangular regions. The complexities of the algorithms are derived, simulation results and error analysis…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
Parametric shape optimization aims at minimizing an objective function f(x) where x are CAD parameters. This task is difficult when f is the output of an expensive-to-evaluate numerical simulator and the number of CAD parameters is large.…
Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be…
Random fields are commonly used for modeling of spatially (or timely) dependent stochastic processes. In this study, we provide a characterization of the intrinsic complexity of a random field in terms of its second order statistics, e.g.,…
Laboratory experiments reveal that variations in bottom topography can qualitatively alter the distribution of randomized surface waves. A normally-distributed, unidirectional wave field becomes highly skewed and non-Gaussian upon…
The present article concerns the stochastic modeling of the turbulent dissipation field and in particular its temporal evolution. To do so, we will be calling for a random distribution, ubiquitous in several aspects of physics and…
In this paper, we study the Casimir effect in a curved spacetime described by gravitational actions quadratic in the curvature. In particular, we consider the dynamics of a massless scalar field confined between two nearby plates and…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…
The observed large-scale structure in our Universe is seen as a result of quantum fluctuations amplified by spacetime evolution. This, and related problems in cosmology, asks for an understanding of the quantum fields of the standard model…
Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated…
Asymptotic properties of a vector of length power functionals of random geometric graphs are investigated. More precisely, its asymptotic covariance matrix is studied as the intensity of the underlying homogeneous Poisson point process…
Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied…
Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently…
Numerical relativity (NR) enables the study of physics in strong and dynamical gravitational fields and provides predictions for the gravitational-wave signals produced by merging black holes. Despite the impressive accuracy of modern…
The Gaussian Free Field (GFF) is a canonical random surface in probability theory generalizing Brownian motion to higher dimensions. In two dimensions, it is critical in several senses, and is expected to be the universal scaling limit of a…
In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fr\'echet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means.…