Related papers: Convergence for varying measures
In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…
Recently, weak measurements were used to measure small effects that are transverse to the propagation direction of a light beam. Here we address the question whether weak measurements are also useful for measuring small longitudinal phase…
This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…
Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are…
The existence of the weak limit as n --> infinity of the uniform measure on rooted triangulations of the sphere with n vertices is proved. Some properties of the limit are studied. In particular, the limit is a probability measure on random…
Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We…
We define an integral of real-valued functions with respect to a measure that takes its values in the extended positive cone of a partially ordered vector space $E$. The monotone convergence theorem, Fatou's lemma, and the dominated…
We characterize real functions $f$ on an interval $(-\alpha,\alpha)$ for which the entrywise matrix function $[a_{ij}] \mapsto [f(a_{ij})]$ is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional…
With the help of a simple variational procedure it is possible to convert the partial sums of order $N$ of many divergent series expansions $f(g)=\sum_{n=0}^\infty a_n g^n$ into partial sums $\sum_{n=0}^N b_n g^{- \omega n}$, where…
We take under consideration Young measures with densities. The notion of density of a Young measure is introduced and illustrated with examples. It is proved that the density of a Young measure is weakly sequentially closed set. In the case…
We study here a sequence of secondary measures, so called because the set of secondary polynomials on a given term become orthogonal for the next measure. The main result is a formula making explicit the density of any term of the sequence,…
We investigate the behavior of sequences $(f(c_nx))$ for Lebesgue integrable functions $f:\mathbb R^d\to\mathbb R$. In particular, we give a~description of classes of multipliers $(c_n)$ and $(d_n)$ such that $f(c_nx)\to0$ or…
In this paper, we explore the limiting weak-type behaviors of some integral operators including maximal operators, singular and fractional integral operators and maximal truncated singular integrals et al. Some optimal limiting weak-type…
Let $A \in M_n(\C)$. We consider the mapping $f_A(x)=x^*Ax$, defined on the unit sphere in $\C^n$. The map has a multi-valued inverse $f_A^{-1}$, and the continuity properties of $f_A^{-1}$ are considered in terms of the structure of the…
For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The convergence takes place in the space of…
We study the constraints on gravity scale $M_P$ in extra-dimension gravitational theory, obtained from gravity-induced processes. The obtained constraints are subdivided into strong (though not robust) and reliable (though less strong). The…
The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When…
We show that under natural growth conditions on the entropy function, convergence in relative entropy is equivalent to $L_p$-convergence. The main tool is the theory of Young measures, in a form that accounts for the formation of…
A review of the state of the art of the comparison between any two different modes of convergence of sequences of measurable functions is carried out with focus on the algebraic structure of the families under analysis. As a complement of…
Concentration of measure is studied, and obtained, for stable and related random vectors.