Related papers: Pairwise optimal coupling of multiple random varia…
Some mathematical theorems represent ideas that are discovered again and again in different forms. One such theorem is Hall's marriage theorem. This theorem is equivalent to several other theorems in combinatorics and optimization theory,…
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…
This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…
For the basic case of $L_2$ optimal transport between two probability measures on a Euclidean space, the regularity of the coupling measure and the transport map in the tail regions of these measures is studied. For this purpose, Robert…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
A coupling of two distributions $P_{X}$ and $P_{Y}$ is a joint distribution $P_{XY}$ with marginal distributions equal to $P_{X}$ and $P_{Y}$. Given marginals $P_{X}$ and $P_{Y}$ and a real-valued function $f$ of the joint distribution…
This paper proves the Baum--Katz theorem for sequences of pairwise independent identically distributed random variables with general norming constants under optimal moment conditions. The proof exploits some properties of slowly varying…
The problem as to when two noncommuting observables are considered to have the same value arises commonly, but shows a nontrivial difficulty. Here, an answer is given by establishing the notion of perfect correlations between noncommuting…
We show that a proportionality between the entanglement Hamiltonian and the Hamiltonian of a subsystem exists near the limit of maximal entanglement under certain conditions. Away from that limit, solvable models show that the coupling…
Often, one would like to determine some observable A, but can only measure some (hopefully related) observable M. This can arise, for example, in quantum eavesdropping, or when the research lab budget isn't large enough for that 100%…
Deterministic extraction of Bell pairs from a finite number of partially entangled pairs is discussed. We derive the maximum number of Bell pairs that can be obtained with probability 1 by local operations and classical communication. It is…
For $N\in\mathbb{N}$, let $\pi_N$ be the law of the number of fixed points of a random permutation of $\{1, 2, ..., N\}$. Let $\mathcal{P}$ be a Poisson law of parameter 1.A classical result shows that $\pi_N$ converges to $\mathcal{P}$ for…
Prior proposals for cumulative statistics suggest making tiny random perturbations to the scores (independent variables in a regression) in order to ensure the scores' uniqueness. Uniqueness means that no score for any member of the…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
We consider the problem of allocating samples to a finite set of discrete distributions in order to learn them uniformly well in terms of four common distance measures: $\ell_2^2$, $\ell_1$, $f$-divergence, and separation distance. To…
String theory predicts that the couplings of Nature descend from dynamical fields. All known string-motivated particle physics models also come with a wide range of possible extra sectors. It is common to posit that such moduli are frozen…
We derive the distribution of the maximum number of common neighbours of a pair of vertices in a dense random regular graph.The proof involves two important steps. One step is to establish the extremal independence property: the asymptotic…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…