Related papers: A robust quantitative local central limit theorem …

By the Lindeberg-L\'evy central limit theorem, standardized partial sums of a sequence of mutually independent and identically distributed random variables converge in law to the standard normal distribution. It is known that mutual…

In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study…

We give a version of the Borel-Cantelli lemma. As an application, we prove an almost sure local central limit theorem. As another application, we prove a dynamical Borel-Cantelli lemma for systems with sufficiently fast decay of…

We provide numerical indications of the $q$-generalised central limit theorem that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics. We focus on $N$ binary random variables correlated in a {\it scale-invariant} way.…

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…

We derive a Gaussian Central Limit Theorem for the sample quantiles based on locally dependent random variables with explicit convergence rate. Our approach is based on converting the problem to a sum of indicator random variables, applying…

We give an FPTAS for computing the number of matchings of size $k$ in a graph $G$ of maximum degree $\Delta$ on $n$ vertices, for all $k \le (1-\delta)m^*(G)$, where $\delta>0$ is fixed and $m^*(G)$ is the matching number of $G$, and an…

The modified massive Arratia flow is a model for the dynamics of passive particle clusters moving in a random fluid that accounts for the effects of mass aggregation. We show a central limit theorem for the point process associated to the…

The Lovasz Local Lemma (LLL) is a probabilistic tool which has been used to show the existence of a variety of combinatorial structures with good "local" properties. The "LLL-distribution" can be used to show that the resulting structures…

We apply Lindeberg's method, invented to prove a central limit theorem, to analyze the moderate deviations around such a central limit theorem. In particular, we will show moderate deviation principles for martingales as well as for random…

We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these…

In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and non irreducible Markov chains…

Consider a discrete-time martingale, and let $V^2$ be its normalized quadratic variation. As $V^2$ approaches 1, and provided that some Lindeberg condition is satisfied, the distribution of the rescaled martingale approaches the Gaussian…

Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…

Randomized block factorial experiments are widely used in industrial engineering, clinical trials, and social science. Researchers often use a linear model and analysis of covariance to analyze experimental results; however, limited studies…

The central limit theorem for convex bodies says that with high probability the marginal of an isotropic log-concave distribution along a random direction is close to a Gaussian, with the quantitative difference determined asymptotically by…

The classic central limit theorem and $\alpha$-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the…

In a paper that appeared in 2010, C. Tone proved a multivariate central limit theorem for some strictly stationary random fields of random vectors satisfying certain mixing conditions. The "normalization" of a given "partial sum" (or "block…

In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a…

We study the distribution of the occurrence of rare patterns in sufficiently mixing Gibbs random fields on the lattice $\mathbb{Z}^d$, $d\geq 2$. A typical example is the high temperature Ising model. This distribution is shown to converge…