Related papers: Limit theorems with rate of convergence under subl…

The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. In particular, special attention is paid…

The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…

The standard central limit theorem plays a fundamental role in Boltzmann-Gibbs statistical mechanics. This important physical theory has been generalized \cite{Tsallis1988} in 1988 by using the entropy $S_q = \frac{1-\sum_i p_i^q}{q-1}$…

We show how recent results by Bening and Korolev in the context of estimation, when linked with a classical result of Fisher concerning the negative binomial distribution, can be used to explain the ubiquity of power law probability…

The Max-Min and Min-Max of matrices arise prevalently in science and engineering. However, in many real-world situations the computation of the Max-Min and Min-Max is challenging as matrices are large and full information about their…

Serfozo (2009, Theorem 2.65) gives a useful central limit theorem for processes with regenerative increments. Unfortunately, there is a gap in the proof. We fill this gap, and at the same time we weaken the assumptions. Furthermore, we give…

A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…

We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…

For $1\le p \le \infty$, the Fr\'echet $p$-mean of a probability measure on a metric space is an important notion of central tendency that generalizes the usual notions in the real line of mean ($p=2$) and median ($p=1$). In this work we…

A uniform law of large numbers and a central limit theorem are established via a martingale approach for a univariate Hawkes process with immigration given by a renewal process. The results are obtained for renewal processes with absolutely…

Random matrices from the elliptic Ginibre orthogonal ensemble (GinOE) are a certain linear combination of a real symmetric, and real anti-symmetric, real Gaussian random matrices and controlled by a parameter $\tau$. Our interest is in the…

This paper re-examines the limit theorems of Abadie and Imbens for nearest-neighbor matching estimators of average treatment effects with a fixed number of matches. We establish, for the first time, a non-normalized central limit theorem…

We establish a central limit theorem for the unnormalized linear statistic of the Gaussian Unitary Ensemble under optimal conditions: the linear statistics converges if and only if the expression for the limiting variance is finite.

This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study…

The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…

A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…

We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling…

We utilize an ergodic theory framework to explore sublinear expectation theory. Specifically, we investigate the pointwise Birkhoff's ergodic theorem for invariant sublinear expectation systems. By further assuming that these sublinear…

We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal…

This paper derives central limit and bootstrap theorems for probabilities that sums of centered high-dimensional random vectors hit hyperrectangles and sparsely convex sets. Specifically, we derive Gaussian and bootstrap approximations for…