Related papers: Limit theorems for inhomogeneous random walks on $…

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…

We obtain non-uniform Berry-Esseen type estimates for several classes of weakly dependent sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or expanding…

We give estimates on the rate of convergence in the Boolean central limit theorem for the L\'evy distance. In the case of measures with bounded support we obtain a sharp estimate by giving a qualitative description of this convergence.

We derive explicit Berry-Esseen bounds in the total variation distance for the Breuer-Major central limit theorem, in the case of a subordinating function $\varphi$ satisfying minimal regularity assumptions. Our approach is based on the…

Linear wavelet density estimators are wavelet projections of the empirical measure based on independent, identically distributed observations. We study here the law of the iterated logarithm (LIL) and a Berry-Esseen type theorem. These…

Motivated by a recent work of Benoist and Quint and extending results from the PhD thesis of the third author, we obtain limit theorems for products of independent and identically distributed elements of GLd (R), such as the…

We provide bounds of Berry-Esseen type for fundamental limit theorems in operator-valued free probability theory such as the operator-valued free Central Limit Theorem and the asymptotic behaviour of distributions of operator-valued…

We show, how the classical Berry-Esseen theorem for normal approximation may be used to derive rates of convergence for random sums of centerd, real-valued random variables with respect to a certain class of probability metrics, including…

This article presents a new proof of the rate of convergence to the normal distribution of sums of independent, identically distributed random variables in chi-square distance, which was also recently studied in \cite{BobkovRenyi}. Our…

We provide a sharp rate of convergence in the central limit theorem for random vectors with an unconditional, log-concave density. The argument relies on analysis of the Neumann laplacian on convex domains and on the theory of optimal…

Let (Zn) be a branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the central limit theorem on logZn by using the…

We adapt Stein's method to obtain Berry--Esseen type error bounds in the multivariate central limit theorem for non-stationary processes generated by time-dependent compositions of uniformly expanding dynamical systems. In a particular case…

We consider random walks conditioned to stay positive. When the mean of increments is zero and variance is finite it is known that they converge to the Rayleigh distribution. In the present paper we derive a Berry-Esseen type estimate and…

We prove Berry-Esseen theorems and the almost sure invariance principle with rates for partial sums of the form $S_n=\sum_{j=0}^{n-1}f_j\circ T_{j-1}\circ\cdots\circ T_1\circ T_0$ where $f_j$ are functions with uniformly bounded…

It is expected that the statistical fluctuations of local observables in large quantum systems obey the central limit theorem, and approximate a normal distribution as their size grows. Here, we prove a version of the Berry-Esseen theorem…

Let $X_1,\ldots,X_N$ be i.i.d.\ random variables distributed like $X$. Suppose that the first $k \geq 3$ moments $\{ \mathbb{E}[X^j] : j = 1,\ldots,k\}$ of $X$ agree with that of the standard Gaussian distribution, that…

In this work the $\ell_q$-norms of points chosen uniformly at random in a centered regular simplex in high dimensions are studied. Berry-Esseen bounds in the regime $1\leq q < \infty$ are derived and complemented by a non-central limit…

Consider the matrix products $G_n: = g_n \ldots g_1$, where $(g_{n})_{n\geq 1}$ is a sequence of independent and identically distributed positive random $d\times d$ matrices. Under the optimal third moment condition, we first establish a…

Let $S_n$ be a random walk with i.i.d. increments which have zero mean and finite variance. For every $x\ge0$ we define the stopping time $\tau_x:=\inf\{n\ge1:x+S_n\le0\}$ and consider the probabilities $\mathbb{P}(x+S_n\ge y,\tau_x>n)$. We…

Two different aspects of parabolic iteration in the complex upper half-plane are considered here. First, from a noncommutative probability perspective, a Berry-Esseen type estimate for the convergence speed of the monotone central limit…