Related papers: Minimum correlation for any bivariate Geometric di…
The problem of calculating real-time correlation functions is formulated in terms of an imaginary-time partial differential equation. The latter is solved analytically for the perturbed harmonic oscillator and compared with the known exact…
In the regression framework, the empirical measure based on the responses resulting from the nearest neighbors, among the covariates, to a given point $x$ is introduced and studied as a central statistical quantity. First, the associated…
We prove that any absolutely continuous probability measure on a high-dimensional linear space has low-dimensional marginals that are approximately spherically-symmetric.
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
Let $G$ be a simple connected graph on $n$ vertices, and let $\lambda_1(G),\lambda_2(G),\ldots,\lambda_n(G)$ be the eigenvalues of its adjacency matrix $A(G)$. For $p>0$, define the $p$-energy of $G$ by $\mathcal E_p(G)=\sum_{i=1}^n…
Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how…
This paper is about interpolating minimal surfaces between two real analytic curves, a and b, each of which are simple real analytic curves, using the Bj\"{o}rling-Schwarz formula in the domain where it is valid, changing the normal…
In this paper we compare the minimums of two independent and heterogeneous samples each following Kumaraswamy-G distribution with the same and the different parent distribution functions. The comparisons are carried out with respect to…
We study the short-time asymptotical behavior of stochastic flows on \mathbb{R} in the \sup-norm. The results are stated in terms of a Gaussian process associated with the covariation of the flow. In case the Gaussian process has a…
In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…
Some simple (namely, single-channel) correlation functions involving an arbitrary number of fields are computed by means of a direct application of the residue calculus, through partial fraction expansions. Examples are presented in minimal…
We study the conditional distribution of zeros of a Gaussian system of random polynomials (and more generally, holomorphic sections), given that the polynomials or sections vanish at a point p (or a fixed finite set of points). The…
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…
George R. Terrell (1983, {Ann. Probab., vol. 11(3), pp. 823--826) showed that the Pearson coefficient of correlation of an ordered pair from a random sample of size two is at most one-half, and the equality is attained only for rectangular…
Spanner constructions focus on the initial design of the network. However, networks tend to improve over time. In this paper, we focus on the improvement step. Given a graph and a budget $k$, which $k$ edges do we add to the graph to…
Let (N,g) be a nilpotent Lie group endowed with an invariant geometric structure (cf. symplectic, complex, hypercomplex or any of their `almost' versions). We define a left invariant Riemannian metric on N compatible with g to be minimal,…