Related papers: The distance problem via subadditivity
For a system consisting of several Dirac fields and a particle, we study the Cauchy problem with random initial data. We assume that the initial measure has zero mean value, a finite mean charge density, a translation-invariant covariance…
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the…
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…
A coefficient is introduced that quantifies the extent of separation of a random variable $Y$ relative to a number of variables $\mathbf{X} = (X_1, \dots, X_p)$ by skillfully assessing the sensitivity of the relative effects of the…
The use of persistent homology in applications is justified by the validity of certain stability results. At the core of such results is a notion of distance between the invariants that one associates with data sets. Here we introduce a…
Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically…
We examine the geometry of the spaces between particles in diffusion-limited cluster aggregation, a numerical model of aggregating suspensions. Computing the distribution of distances from each point to the nearest particle, we show that it…
The distance conjecture diagnoses viable low-energy effective realisation of consistent theories of quantum gravity by examining their breakdown at infinite distance in their parameter space. At the same time, infinite distance points in…
We define a special network that exhibits the large embeddings in any class of similar algebras. With the aid of this network, we introduce a notion of distance that conceivably counts the minimum number of dissimilarities, in a sense,…
We consider some general facts concerning convergence P_{n}-Q_{n}\to 0 as n\to \infty, where P_{n} and Q_{n} are probability measures in a complete separable metric space. The main point is that the sequences {P_{n}} and {Q_{n}} are not…
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…
We develop a unified framework for nonlinear subdivision schemes on complete metric spaces (CMS). We begin with CMS preliminaries and formalize refinement in CMS, retaining key structural properties, such as locality. We prove a convergence…
Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…
A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…
Upper bounds for the $L_p$-discrepancies of point distributions in compact metric measure spaces for $0<p\le\infty$ have been established in the paper [6] by Brandolini, Chen, Colzani, Gigante and Travaglini. In the present paper we show…
We study the problem of predicting numeric labels that are constrained to the integers or to a subrange of the integers. For example, the number of up-votes on social media posts, or the number of bicycles available at a public rental…
We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establish a new rate of convergence of the $\infty-$Wasserstein…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
We are concerned with the general problem of proving the existence of joint distributions of two discrete random variables $M$ and $N$ subject to infinitely many constraints of the form $\mathbb{P}\left(M=i,N=j\right)=0$. In particular, the…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…