Related papers: A central limit theorem for integrals of random wa…

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 study a random partial covering model on the $(d-1)$-dimensional unit sphere, where $N$ spherical caps are placed independently and uniformly at random, each covering a surface fraction of $1/N$. This model provides a continuous…

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…

This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic…

We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…

We prove a local limit theorem, i.e. a central limit theorem for densities, for a sequence of independent and identically distributed random variables taking values on an abstract Wiener space; the common law of those random variables is…

We consider compact Grassmann manifolds $G/K$ over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type $BC$. From an explicit integral representation of these polynomials we deduce a…

Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including in signal processing, data aggregation and network sensing. Adding random noise to these scenarios, as is natural…

We establish a central limit theorem for the central values of Dirichlet $L$-functions with respect to a weighted measure on the set of primitive characters modulo $q$ as $q \rightarrow \infty$. Under the Generalized Riemann Hypothesis…

We give a new proof of the classical Central Limit Theorem, in the Mallows ($L^r$-Wasserstein) distance. Our proof is elementary in the sense that it does not require complex analysis, but rather makes use of a simple subadditive inequality…

There is a well understood way of generating random coverings of a fixed manifold by sampling homomorphisms from the fundamental group of this manifold into the symmetric group. We prove a central limit theorem for the number of connected…

This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of…

We prove multi-dimensional central limit theorems for the spectral moments (of arbitrary degrees) associated with random matrices with real-valued i.i.d. entries, satisfying some appropriate moment conditions. Our techniques rely on a…

In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…

This paper investigates a local central limit theorem for a normalized sequence of random variables belonging to a fixed order Wiener chaos and converging to the standard normal distribution. We prove, without imposing any additional…

We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions…

We revisit the central limit theorem for integrated periodograms, equivalently for Toeplitz quadratic forms of stationary Gaussian sequences. Under a regular-variation assumption allowing long-memory singularities and slowly varying…

The de Moivre-Laplace theorem is a special case of the central limit theorem for Bernoulli random variables, and can be proved by direct computation. We deduce the central limit theorem for any random variable with finite variance from the…

As generalizations of random graphs, random simplicial complexes have been receiving growing attention in the literature. In this paper, we naturally extend the Random Connection Model (RCM), a random graph that has been extensively studied…

Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as {\lambda} tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spectral projector of the Laplacian onto functions with…