相关论文: On the relationship between mean observations, spa…
Motivated by the simulation of stable random fields, we consider the issue of discrete approximations of independently scattered stable noise. Two approaches are proposed: grid approximations available when the underlying space is $\bbR^d$…
We study different ways of determining the mean distance $ < r_n >$ between a reference point and its $n$-th neighbour among random points distributed with uniform density in a $D$-dimensional Euclidean space. First we present a heuristic…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…
We point out a new possibility to determine the average redshift distribution of a large sample of gravitational wave standard sirens, without spectroscopic follow-ups. It is based on the cross correlation between the luminosity-distance…
Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…
In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a…
Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses…
These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kinetic models derived as continuum versions of second order…
We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field, and that of a normal vector with a positive definite covariance matrix. Our bounds are commensurate to the…
The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
A new method is applied for deriving the redshift and shadow of a Schwarzschild black hole moving freely in the de Sitter expanding universe as recorded by a co-moving remote observer. This method is manly algebraic focusing on the…
We study the influence of higher curvature effects on stellar structure and conclude that the properties of stars are greatly impacted when such terms are dynamic. In particular the surface gravitational redshift which is connected to the…
In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space $\mathbb{R}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of…
A method for constructing statistically homogeneous and isotropic perfect fluid universe models with significant cosmic backreaction is proposed. The method is illustrated using a simplified model constructed as a Swiss-cheese model with…
We discuss how the redshift (Mattig) method in Friedmann cosmology relates to dynamical distance indicators based on Newton's gravity (Teerikorpi 2011). It belongs to the class of indicators where the relevant length inside the system is…
In this methodological note we discuss several topics related to interpretation of some basic cosmological principles. We demonstrate that one of the key points is the usage of synchronous reference frames. The Friedmann-Robertson-Walker…
Current cosmological observations, when interpreted within the framework of a homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) model, strongly suggest that the Universe is entering a period of accelerating expansion.…
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
Two distinct non-singular interior models that describe anisotropic spherical configurations are presented in this work. We develop the Einstein field equations and the associated mass function in accordance with a static spherical…