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We present a central limit theorem for stationary random fields that are short-range dependent and asymptotically independent. As an application, we present a central limit theorem for an infinite family of interacting It\^o-type diffusion…

Probability · Mathematics 2021-10-19 Le Chen , Davar Khoshnevisan , David Nualart , Fei Pu

We consider N single server infinite buffer queues with service rate \beta. Customers arrive at rate N\alpha, choose L queues uniformly, and join the shortest. We study the processes R^N for large N, where R^N_t(k) is the fraction of queues…

Probability · Mathematics 2007-05-23 Carl Graham

We deduce sufficient conditions for the Central Limit Theorem (CLT) in the Lebesgue-Riesz space L(p) defined on some measure space for the sequence of centered random variables satisfying the strong mixing (Rosenblatt) condition. We…

Probability · Mathematics 2019-12-05 M. R. Formica , E. Ostrovsky , L. Sirota

In this paper we establish a general dynamical Central Limit Theorem (CLT) for group actions which are exponentially mixing of all orders. In particular, the main result applies to Cartan flows on finite-volume quotients of simple Lie…

Dynamical Systems · Mathematics 2017-06-29 Michael Björklund , Alexander Gorodnik

We consider sequences of $U$-processes based on symmetric kernels of a fixed order, that possibly depend on the sample size. Our main contribution is the derivation of a set of analytic sufficient conditions, under which the aforementioned…

Probability · Mathematics 2022-03-16 Christian Döbler , Mikołaj Kasprzak , Giovanni Peccati

A blocks method is used to define clusters of extreme values in stationary time series. The cluster starts at the first large value in the block and ends at the last one. The block cluster measure (the point measure at clusters) encodes…

Statistics Theory · Mathematics 2023-09-01 Zaoli Chen , Rafal Kulik

In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes…

Statistics Theory · Mathematics 2007-06-13 Jean-Marc Bardet , Paul Doukhan , Gabriel Lang , Nicolas Ragache

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

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…

Probability · Mathematics 2022-02-11 Michael Fleermann , Werner Kirsch

A recent result by Barrera and Peligrad shows that the quenched Central Limit Theorem holds for the discrete Fourier transforms (DFT) of a stationary process in $L^2$ if a "random" centering is used. In this note we show that this is a…

Probability · Mathematics 2014-11-12 David Barrera

For $\Delta \ge 5$ and $q$ large as a function of $\Delta$, we give a detailed picture of the phase transition of the random cluster model on random $\Delta$-regular graphs. In particular, we determine the limiting distribution of the…

Probability · Mathematics 2021-09-16 Tyler Helmuth , Matthew Jenssen , Will Perkins

Cluster Dynamical Mean Field Theories are analyzed in terms of their semiclassical limit and their causality properties, and a translation invariant formulation of the cellular dynamical mean field theory, PCDMFT, is presented. The…

Strongly Correlated Electrons · Physics 2009-11-10 G. Biroli , O. Parcollet , G. Kotliar

We formulate and prove a new sufficient conditions for Central Limit Theorem(CLT) in the space of continuous functions in the terms typical for the approximation theory. We prove that the conditions for continuous CLT obtained by N.C.Jain…

Probability · Mathematics 2013-04-02 E. Ostrovsky , L. Sirota

The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edges are independently drawn with probability depending on the locations of the two end…

Probability · Mathematics 2021-02-18 Van Hao Can , Khanh Duy Trinh

We produce a series of Central Limit Theorems (CLTs) associated to compact metric measure spaces $(K,d,\eta)$, with $\eta$ a reasonable probability measure. For the first CLT, we can ignore $\eta$ by isometrically embedding $K$ into…

Probability · Mathematics 2020-01-14 Steven Rosenberg , Jie Xu

We consider empirical multi-dimensional Rare Events Point Processes that keep track both of the time occurrence of extremal observations and of their severity, for stochastic processes arising from a dynamical system, by evaluating a given…

Dynamical Systems · Mathematics 2017-09-19 Ana Cristina Moreira Freitas , Jorge Milhazes Freitas , Mário Magalhães

In this article we prove a new central limit theorem (CLT) for coupled particle filters (CPFs). CPFs are used for the sequential estimation of the difference of expectations w.r.t. filters which are in some sense close. Examples include the…

Statistics Theory · Mathematics 2026-01-14 Ajay Jasra , Fangyuan Yu

We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all…

Probability · Mathematics 2010-11-08 Magda Peligrad , Wei Biao Wu

This work improves the existing central limit theorems (CLTs) for geometric functionals of Gibbs processes in three aspects. First, we derive a CLT for weakly stabilizing functionals, thereby improving on the previously used assumption of…

Probability · Mathematics 2024-06-12 Christian Hirsch , Moritz Otto , Anne Marie Svane

In this paper we consider a superprocess being a measure-valued diffusion corresponding to the equation $u_{t}=Lu+\alpha u-\beta u^{2}$, where $L$ is the infinitesimal operator of the \emph{Ornstein-Uhlenbeck process} and…

Probability · Mathematics 2012-04-02 Piotr Miłoś