Related papers: The Berry-Esseen Theorem for Circular $\beta$-ense…
Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including in signal processing, data aggregation and network sensing. Adding random noise to these scenarios, as is natural…
Using the subordination approach, we provide a new Berry-Esseen-type estimate in the free central limit theorem in terms of the fourth Lyapunov fraction. In the special case of identical distributions, our result implies a rate of order…
We prove an operator level limit for the circular Jacobi $\beta$-ensemble. As a result, we characterize the counting function of the limit point process via coupled systems of stochastic differential equations. We also show that the…
Let $(Z_n)$ be a supercritical branching process in a random environment $\xi = (\xi_n)$. We establish a Berry-Esseen bound and a Cram\'er's type large deviation expansion for $\log Z_n$ under the annealed law $\mathbb P$. We also improve…
We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type…
This paper studies the asymptotic distribution of descents $\des(w)$ in a permutation $w$, and its inverse, distributed according to the Mallows measure. The Mallows measure is a non-uniform probability measure on permutations introduced to…
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…
New nonuniform Berry--Esseen-type bounds for sums of independent random variables are obtained, motivated by recent studies concerning such bounds for nonlinear statistics. The proofs are based on the Chen--Shao concentration techniques…
We obtain a sharp estimate of the speed of convergence in the Boolean central limit theorem for measures of finite sixth moment. The main tool is a quantitative version of the Stieltjes-Perron inversion formula.
Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We…
Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a…
Let {F_n} be a normalized sequence of random variables in some fixed Wiener chaos associated with a general Gaussian field, and assume that E[F_n^4] --> E[N^4]=3, where N is a standard Gaussian random variable. Our main result is the…
There have been, over the last 8 years, a number of far reaching extensions of the famous original F. and M. Riesz's uniqueness theorem that states that if a bounded analytic function in the unit disc of the complex plane $\Bbb C$ has the…
We analyze the quality of the gaussian approximation to linear combinations of n independent, identically-distributed random variables with finite fourth moments. It turns out that there exist universal, simple linear combinations that…
We prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the…
For any $\beta > 1$, let $T_\beta: [0,1)\rightarrow [0,1)$ be the $\beta$-transformation defined by $T_\beta x=\beta x \mod 1$. We study the uniform recurrence properties of the orbit of a point under the $\beta$-transformation to the point…
A new Berry-Esseen bound for non-linear functionals of non-symmetric and non-homogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin-Stein method and an analysis of the discrete…
Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a functional, an estimate for different probability distances…
The Beta coalescents are stochastic processes modeling the genealogy of a population. They appear as the rescaled limits of the genealogical trees of numerous stochastic population models. In this article, we take interest in the number of…
We prove a Central Limit Theorem for probability measures defined via the variation of the sum-of-digits function, in base $b\ge 2$. For $r\ge 0$ and $d \in \mathbb{Z}$, we consider $\mu^{(r)}(d)$ as the density of integers $n\in…