This study presents a novel technique to estimate the computational complexity of sequential decoding using the Berry-Esseen theorem. Unlike the theoretical bounds determined by the conventional central limit theorem argument, which often holds only for sufficiently large codeword length, the new bound obtained from the Berry-Esseen theorem is valid for any blocklength. The accuracy of the new ...

By Louis H.Y. Chen † and Qi-Man Shao ‡ National University of Singapore and University of Oregon §¶ We establish both uniform and non-uniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper than many existing ones in the literature. The proofs cou...

In this paper, the authors investigate the Berry-Esseen bounds of weighted kernel estimator for a nonparametric regression model based on linear process errors under a LNQD random variable sequence. The rate of the normal approximation is shown as [Formula: see text] under some appropriate conditions. The results obtained in the article generalize or improve the corresponding ones for mixing de...

We consider the random walk among random conductances on Z. We assume that the conductances are independent, identically distributed and uniformly bounded away from 0 and infinity. We obtain a quantitative version of the central limit theorem for this random walk, which takes the form of a Berry-Esseen estimate with speed t−1/10 for d 6 2, and speed t−1/5 for d > 3, up to logarithmic corrections.

For a supercritical branching process (Zn) in a stationary and ergodic environment ξ, we study the rate of convergence of the normalized population Wn = Zn/E[Zn|ξ] to its limitW∞: we show a central limit theorem forW∞−Wn with suitable normalization and derive a Berry-Esseen bound for the rate of convergence in the central limit theorem when the environment is independent and identically distrib...

We study the number of subtrees on the fringe of random recursive trees and random binary search trees whose limit law is known to be either normal or Poisson or degenerate depending on the size of the subtree. We introduce a new approach to this problem which helps us to further clarify this phenomenon. More precisely, we derive optimal Berry-Esseen bounds and local limit theorems for the norm...

We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians of N spins arranged on a ddimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up toO(N) spins. The proof rests on a...