Related papers: Variance estimates and almost Euclidean structure
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Modelling cosmic voids as spheres in Euclidean space, the notion of a de-Sitter configuration space is introduced. It is shown that a uniform distribution over this configuration space yields a power-law approximating the void size…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…
Let X Nv(0, {\Lambda}) be a normal vector in v dimensions, where {\Lambda} is diagonal. With reference to the truncated distribution of X on the interior of a v-dimensional Euclidean ball, we completely prove a variance inequality and a…
In this paper, we present an analytical study of the relationship between the statistical distribution of a physical parameter and the uncertainties in the physical quantities used to determine it through indirect measurement. We…
In this paper we propose a method to construct probability measures on the space of convex bodies with a given pushforward distribution. Concretely we show that there is a measure on the metric space of centrally symmetric convex bodies,…
A strong law of large numbers for $d$-dimensional random projections of the $n$-dimensional cube is derived. It shows that with respect to the Hausdorff distance a properly normalized random projection of $[-1,1]^n$ onto $\mathbb{R}^d$…
We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research…
Poincar{\'e} inequalities are ubiquitous in probability and analysis and have various applications in statistics (concentration of measure, rate of convergence of Markov chains). The Poincar{\'e} constant, for which the inequality is tight,…
We investigate the statistical distribution of Newtonian gravitational forces acting on a test particle embedded in an infinite, homogeneous, and uncorrelated random gas of point masses. Using order statistics, we derive the probability…
The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
This article investigates sharp comparison of moments for various classes of random variables appearing in a geometric context. In the first part of our work we find the optimal constants in the Khintchine inequality for random vectors…
Log-concave distributions include some important distributions such as normal distribution, exponential distribution and so on. In this note, we show inequalities between two Lp-norms for log-concave distributions on the Euclidean space.…
Many generic results have been proved, especially concerning the qualitative behaviour of solutions of partial differential equations. Recently, a new notion of "almost always", the prevalence, has been developped for vectorial spaces. This…
We establish uniform estimates for order statistics of sequences of independent identically distributed random variables with log-concave distribution in terms of Orlicz norms associated with the distribution function of the random…
We study the approximation of arbitrary distributions $P$ on $d$-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback--Leibler-type functional. We show that such an approximation exists if…
We study the asymptotic behavior of the fluctuations of smooth and rough linear statistics for determinantal point processes on the sphere and on the Euclidean space. The main tool is the generalization of some norm representation results…
In this paper, a new statistic feature of the discrete short-time amplitude spectrum is discovered by experiments for the signals of unvoiced pronunciation. For the random-varying short-time spectrum, this feature reveals the relationship…