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We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in $\mathbb{R}^d$. This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998)…

Probability · Mathematics 2007-05-23 Lothar Heinrich , Hendrik Schmidt , Volker Schmidt

Lacunary function systems of type $(f(M_nx))_{n\geq 1}$ for periodic functions $f$ and sequences of fast-growing matrices $(M_n)_{n\geq 1}$ exhibit many properties of independent random variables like satisfying the Central Limit Theorem or…

Probability · Mathematics 2014-08-12 Thomas Löbbe

We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than $\epsilon$ ($\epsilon$ > 0). Is is known ([BM05]) that the empirical measure of these fragments converges in law, under some…

Probability · Mathematics 2019-07-30 Sylvain Rubenthaler

In this article we formulate the CLT associated to Gaussian operators of type B -- see \cite{BEH15}, where important role is played by colored pair partitions. Then we present a certain family of noncommutative random matrix models for the…

Probability · Mathematics 2017-09-20 Wiktor Ejsmont

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…

Statistical Mechanics · Physics 2009-11-10 Michael Hartmann , Guenter Mahler , Ortwin Hess

We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…

Probability · Mathematics 2015-04-07 Paul Jung , Takashi Owada , Gennady Samorodnitsky

We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…

Probability · Mathematics 2021-04-21 Michael Röckner , Longjie Xie

We investigate the fluctuations of the stochastic Becker-D\"oring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a…

Probability · Mathematics 2018-02-26 Wen Sun

A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…

Mathematical Physics · Physics 2007-05-23 Paul Doukhan , Gabriel Lang , Sana Louhichi , Bernard Ycart

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

We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by…

Probability · Mathematics 2025-01-30 Thomas Deschatre , Pierre Gruet , Antoine Lotz

We study the thermodynamic properties of the generalized non-convex multispecies Curie-Weiss model, where interactions among different types of particles (forming the species) are encoded in a generic matrix. For spins with a generic prior…

Mathematical Physics · Physics 2025-02-28 Francesco Camilli , Emanuele Mingione , Godwin Osabutey

We consider a family of linear operators, diagonalized by the Hankel transform. The Fredholm determinants of these operators, restricted to $L_2[0, R]$, are expressed in a convenient form for asymptotic analysis as $R\to\infty$. The result…

Functional Analysis · Mathematics 2025-04-15 Sergei M. Gorbunov

We consider eigenvalues of generalized Wishart processes as well as particle systems, of which the empirical measures converge to deterministic measures as the dimension goes to infinity. In this paper, we obtain central limit theorems to…

Probability · Mathematics 2019-08-12 Jian Song , Jianfeng Yao , Wangjun Yuan

We obtain the empirical strong law of large numbers, empirical Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general…

Statistics Theory · Mathematics 2020-11-23 Yaozhong Hu , Junxi Zhang

We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying L\'{e}vy measures. The limit process is a new class of symmetric stable…

Probability · Mathematics 2015-01-16 Takashi Owada , Gennady Samorodnitsky

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

Probability · Mathematics 2016-12-13 Li Wang

We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions…

Probability · Mathematics 2014-09-26 Herold Dehling , Olivier Durieu , Marco Tusche

We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and…

Dynamical Systems · Mathematics 2017-11-06 Jacopo De Simoi , Carlangelo Liverani

A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…

Probability · Mathematics 2024-09-17 Abdollah Jalilian , Arnaud Poinas , Ganggang Xu , Rasmus Waagepetersen