Related papers: A generalization of the Lindeberg principle
We derive a central limit theorem for sums of a function of independent sums of independent and identically distributed random variables. In particular we show that previously known result from Rempa\la and Weso\lowski (Statist. Probab.…
In this paper, a connection between bi-free probability and the asymptotics of random quantum channels and tensor products of random matrices is established. Using bi-free matrix models, it is demonstrated that the spectral distribution of…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…
By the Lindeberg principle, we develop in this paper an approximation to one dimensional (possibly) asymmetric $\alpha$-stable distributions with $\alpha \in (0,2)$ in the smooth Wasserstein distance. It is the first time that the general…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
In this paper additive bi-free convolution is defined for general Borel probability measures, and the limiting distributions for sums of bi-free pairs of selfadjoint commuting random variables in an infinitesimal triangular array are…
We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…
We extend the spectral method for proving limit theorems to random non-uniformly expanding dynamical systems. This yields the CLT and moderate deviations principles (MDP). We show that as the amount of non-uniformity decreases the CLT rates…
The theory of random matrices contains many central limit theorems. We have central limit theorems for eigenvalues statistics, for the log-determinant and log-permanent, for limiting distribution of individual eigenvalues in the bulk, and…
This paper first surveys the connection of integrable systems of the Painleve type to various distribution functions appearing in Wigner-Dyson random matrix theory. A short discussion is then given of the appearance of these same…
When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…
In this letter we present the inversion of the Mermin-Wagner theorem on graphs, by proving the existence of spontaneous magnetization at finite temperature for classical spin models on transient on the average (TOA) graphs, i.e. graphs…
The aim of the present paper is to establish the multidimensional counterpart of the \textit{fourth moment criterion} for homogeneous sums in independent leptokurtic and mesokurtic random variables (that is, having positive and zero fourth…
The present paper is devoted to possible generalizations of the classic Lagrange Mean Value Theorem. We consider a real-valued function of several variables that is only assumed to be continuous. The main concept is to replace the notion of…
The product of any number of Legendre functions, under a restricted domain, can be expanded by the corresponding Legendre polynomials, with the coefficient being the sinc function. While an analogous expansion can be made for any number of…
Quantitative multivariate central limit theorems for general functionals of possibly non-symmetric and non-homogeneous infinite Rademacher sequences are proved by combining discrete Malliavin calculus with the smart path method for normal…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
A recent development in random matrix theory, the intrinsic freeness principle, establishes that the spectrum of very general random matrices behaves as that of an associated free operator. This reduces the study of such random matrices to…
In earlier work we showed that the particle displacement for the multidimensional periodic Lorentz gas, in the limit of low scatterer density (Boltzmann-Grad limit), satisfies a central limit theorem with superdiffusive scaling. The present…
We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue…