Related papers: Weak Convergence (IA). Sequences of Random Vectors

Using a coupling argument, we establish a general weak law of large numbers for functionals of binomial point processes in d-dimensional space, with a limit that depends explicitly on the (possibly non-uniform) density of the point process.…

We prove the asymptotic independence of the empirical process $\alpha_n = \sqrt{n}( F_n - F)$ and the rescaled empirical distribution function $\beta_n = n (F_n(\tau+\frac{\cdot}{n})-F_n(\tau))$, where $F$ is an arbitrary cdf,…

This article studies the weak convergence and associated Central Limit Theorem for blurring and nonblurring processes. Then, they are applied to the estimation of location parameter. Simulation studies show that the location estimation…

Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…

We connect the weak measurements framework to the path integral formulation of quantum mechanics. We show how Feynman propagators can in principle be experimentally inferred from weak value measurements. We also obtain expressions for weak…

For each $n$, let $U_n$ be Haar distributed on the group of $n\times n$ unitary matrices. Let $\bfx_{n,1},\ldots,\bfx_{n,m} $ denote orthogonal nonrandom unit vectors in ${\Bbb C}^n$ and let $\text{\bf…

For a strictly stationary sequence of $\mathbb{R}_{+}^{d}$--valued random vectors we derive functional convergence of partial maxima stochastic processes under joint regular variation and weak dependence conditions. The limit process is an…

In this paper we introduce several natural definitions of asymptotic independence of two sequences of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak…

The variance of primes in short intervals relates to the Riemann Hypothesis, Montgomery's Pair Correlation Conjecture and the Hardy--Littlewood Conjecture. In regards to its asymptotics, very little is known unconditionally. We study the…

Weakly almost i.i.d. quantum sources are sequences of multipartite states whose fixed-size marginals converge, on average, to tensor powers of a reference state, while allowing arbitrary global correlations and entanglement. We establish…

We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…

In quantum theory, a weak value is a complex number with a somewhat technical definition: it is a ratio whose numerator is the matrix element of a self-adjoint operator and whose denominator is the inner product of a corresponding pair of…

This is an exposition on supercyclicity and weak supercyclicity, especially designed to advance further developments in weakly supercyclicity, which is a recent research field showing significant momentum during the past two decades. For…

Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…

If multiway cluster-robust standard errors are used routinely in applied economics, surprisingly few theoretical results justify this practice. This paper aims to fill this gap. We first prove, under nearly the same conditions as with…

Firstly, we invoke the weak convergence (resp. strong convergence) of translated basic methods involving nonexpansive operators to establish the weak convergence (resp. strong convergence) of the associated method with both perturbation and…

In this paper, we study on weak $I^K$-Cauchy condition as a generalization of weak $I^*$-Cauchy condition in a normed space. We investigate the relationship between weak $I$-Cauchy and weak $I^K$-Cauchy sequences using $AP(I,K)$-condition.…

This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning,…

Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…

We study the weak convergence of iterates of so-called centred kernel quadratic stochastic operators. These iterations, in a population evolution setting, describe the additive perturbation of the arithmetic mean of the traits of an…