We prove a Berry–Esseen theorem, local central limit theorem and (local) large (global) moderate deviations principles for i.i.d. (uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times. Using existing results the problem is reduced to certain (Young) tower extensions, which main focus of this paper. On towers we will obtain our using contraction proper...

In this paper, we establish optimal Berry–Esseen bounds for the generalized U-statistics. The proof is based on a new theorem exchangeable pair approach by Stein’s method under general linearity condition setting. As applications, an convergence rate of normal approximation subgraph counts in Erdos?–Rényi graphs and graphon-random graph obtained.

Berry–Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.

This paper proves a Berry–Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n) as n→∞, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n) is not known even under an exponential strong mixing ...

Abstract In this work the $\ell_q$ -norms of points chosen uniformly at random in a centered regular simplex high dimensions are studied. Berry–Esseen bounds regime $1\leq q < \infty$ derived and complemented by non-central limit theorem together with moderate large deviations case where $q=\infty$ . An application to intersection volume an $\ell_p^n$ -ball is also carried out.

This paper develops techniques to study the asymptotic distribution of number descents in random permutations. We relax an assumption Berry-Esseen theorem Bolthausen (1982) extend theorem's scope martingale differences time-dependent variances. present its applications other combinatorial statistics as they satisfy certain recurrence relation conditions. These include inversions, signed permuta...

A general moment bound for sums of products of Gaussian vector’s functions extending the moment bound in Taqqu (1977, Lemma 4.5) is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non-stationary Gaussian sequences is proved. This theorem extends the previous results of Breuer and Major (1981), Arcones (1994) and others. A Berry-Ess...