Related papers: Statistics of Peaks in Chi-Squared Fields
We investigate distributional properties of a class of spectral spatial statistics under irregular sampling of a random field that is defined on $\mathbb{R}^d$, and use this to obtain a test for isotropy. Within this context, edge effects…
We study the probability distribution of the maximum $M_S $ of a smooth stationary Gaussian field defined on a fractal subset $S$ of $\R^n$. Our main result is the equivalent of the asymptotic behavior of the tail of the distribution…
Linear combinations of chi square random variables occur in a wide range of fields. Unfortunately, a closed, analytic expression for the pdf is not yet known. As a first result of this work, an explicit analytic expression for the density…
We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the…
We study the reconstruction of bandlimited fields from samples taken at unknown but statistically distributed sampling locations. The setup is motivated by distributed sampling where precise knowledge of sensor locations can be difficult.…
We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…
The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of normalized unbounded semigroups.
Enhancement of global symmetry and supersymmetry in the infrared is one of the most intriguing phenomena in quantum field theory. We investigate such phenomena in a large class of three dimensional superconformal field theories, known as…
We report the experimental observation of the bifurcation at the origin of localization of the deformation in a granular material submitted to uniaxial compression. We present a quantitative characterization of the heterogeneity in the…
Researchers routinely characterize optical samples by computing the scattering cross-section. However, the experimental determination of this magnitude requires the measurement and integration of the components of the scattered field in all…
Level statistics is a crucial tool in the exploration of localization physics. The level spacing distribution of the disordered localized phase follows Poisson statistics, and many studies naturally apply it to the quasiperiodic localized…
We introduce the notion of a bivariate random discrete copula on an equidistant mesh and explore its stochastic properties. A random discrete copula is a discrete random field, hence, its value at a given point on the mesh is a random…
We investigate the conditions under which cosmological variations in physical `constants' and scalar fields are detectable on the surface of local gravitationally-bound systems, such as planets, in non-spherically symmetric background…
We study grain boundaries between striped phases in the prototypical Swift-Hohenberg equation. We propose an analytical and numerical far-field-core decomposition that allows us to study existence and bifurcations of grain boundaries…
We have defined pinning fields as those random fields that keep some of the magnetic moments unreversed in the region of negative external applied field during the demagnetizing process. An analysis of the statistical properties of such…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…
It is demonstrated how to represent asymptotically mean stationary (AMS) random sources with values in standard spaces as mixtures of ergodic AMS sources. This an extension of the well known decomposition of stationary sources which has…
The initial conditions of cosmological simulations are commonly drawn from a Gaussian ensemble. The limited number of modes inside a simulation volume gives rise to statistical fluctuations known as \textit{sample variance}, limiting the…
Quasinormal modes describe the relaxation of perturbed black holes and relate ringdown observables to the background geometry. In this work we study the problem in a de Sitter setting within a generalized Proca branch that generates an…
Spontaneous symmetry breaking is a fundamental notion in modern physics, ranging from high energy to condensed matter. However, the usual spontaneous symmetry breaking only considers the equal probability to select the vacua. In this work,…