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The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

Logic in Computer Science · Computer Science 2026-03-10 Henning Basold , Oisín Flynn-Connolly , Chase Ford , Hao Wang

In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and…

Probability · Mathematics 2014-09-22 Yan-Xia Ren , Renming Song , Rui Zhang

We consider a borderline case: the central limit theorem for a strictly stationary time series with infinite variance but a Gaussian limit. In the iid case a well-known sufficient condition for this central limit theorem is regular…

Probability · Mathematics 2025-03-24 Muneya Matsui , Thomas Mikosch

We study some sufficient conditions imposed on the sequence of martingale differences (m.d.) in the separable Banach spaces of continuous functions defined on the metric compact set for the Central Limit Theorem in this space. We taking…

Probability · Mathematics 2014-11-11 L. Sirota

We prove a central limit theorem for stationary multiple (random) fields of martingale differences $f\circ T_{\underline{i}}$, $\underline{i}\in \Bbb Z^d$, where $T_{\underline{i}}$ is a $\Bbb Z^d$ action. In most cases the multiple…

Probability · Mathematics 2018-03-28 Dalibor Volny

We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of random matrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two…

Mathematical Physics · Physics 2007-11-13 M. Shcherbina

This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…

Statistics Theory · Mathematics 2019-12-16 Zeng Li , Qinwen Wang , Runze Li

In this paper, we establish the central limit theorem (CLT) for the linear spectral statistics (LSS) of sample correlation matrix $R$, constructed from a $p\times n$ data matrix $X$ with independent and identically distributed (i.i.d.)…

Probability · Mathematics 2024-09-20 Yanpeng Li , Guangming Pan , Jiahui Xie , Wang Zhou

Combining cross-section and time series data is a long and well established practice in empirical economics. We develop a central limit theory that explicitly accounts for possible dependence between the two data sets. We focus on common…

Methodology · Statistics 2022-09-20 Jinyong Hahn , Guido Kuersteiner , Maurizio Mazzocco

For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a generalized notion of prior does such an equivalence carry over…

Statistics Theory · Mathematics 2022-12-27 Haosui Duanmu , Daniel M. Roy , David Schrittesser

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.

Probability · Mathematics 2015-10-14 Phil Kopel

This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…

Probability · Mathematics 2019-08-08 Guido M. Kuersteiner

General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…

High dimensional central limit theorems (the CLTs) have been extensively studied in recent years under a variety of sufficient moment conditions connecting the dimension growth rate with the tail decay rate. In this article, we investigate…

Probability · Mathematics 2025-12-30 Debraj Das , Soumendra Lahiri

We give a simple and general central limit theorem for a triangular array of m-dependent variables. The result requires only a Lindeberg condition and avoids unnecessary extra conditions that have been used earlier. The result applies also…

Probability · Mathematics 2021-08-30 Svante Janson

The main objective of this article is to establish a central limit theorem for additive three-variable functionals of bifurcating Markov chains. We thus extend the central limit theorem under point-wise ergodic conditions studied in…

Probability · Mathematics 2022-07-04 S. Valère Bitseki Penda

In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower…

Probability · Mathematics 2011-05-24 Magda Peligrad

We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and…

Probability · Mathematics 2015-06-12 Florent Benaych-Georges , Alice Guionnet , Camille Male

In this paper we consider a dynamic Erd\H{o}s-R\'{e}nyi random graph with independent identically distributed edge processes. Our aim is to describe the joint evolution of the entries of a subgraph count vector. The main result of this…

Probability · Mathematics 2025-12-01 Rajat Subhra Hazra , Nikolai Kriukov , Michel Mandjes

Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…

Probability · Mathematics 2026-02-20 Christian Hirsch , Kyeongsik Nam , Moritz Otto