Related papers: A Sharp Rate of Convergence in the Functional Cent…

We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By…

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…

Fitting experiment data onto a curve is a common signal processing technique to extract data features and establish the relationship between variables. Often, we expect the curve to comply with some analytical function and then turn data…

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…

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate…

Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including…

We consider sequences of symmetric $U$-statistics, not necessarily Hoeffding-degenerate, both in a one- and multi-dimensional setting, and prove quantitative central limit theorems (CLTs) based on the use of {\it contraction operators}. Our…

In this work we study and establish some quenched functional Central Limit Theorems (CLTs) for stationary random fields under a projective criteria. These results are functional generalizations of the theorems obtained by Zhang et al.…

We give a two-dimensional central limit theorem (CLT) for the second-order quadratic variation of the centered Gaussian processes on $[0,T]$. Though the approach we use is well known in the literature, the conditions under which the CLT…

This paper investigates the rate of convergence for the central limit theorem of linear spectral statistic (LSS) associated with large-dimensional sample covariance matrices. We consider matrices of the form ${\mathbf…

In this paper, we investigate the functional central limit theorem for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation…

The objective of this study is to investigate the limiting behavior of a subgraph counting process. The subgraph counting process we consider counts the number of subgraphs having a specific shape that exist outside an expanding ball as the…

We consider a class of self-similar, continuous Gaussian processes that do not necessarily have stationary increments. We prove a version of the Breuer-Major theorem for this class, that is, subject to conditions on the covariance function,…

We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…

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…

We prove two theorems related to the Central Limit Theorem (CLT) for Martin-L\"of Random (MLR) sequences. Martin-L\"of randomness attempts to capture what it means for a sequence of bits to be "truly random". By contrast, CLTs do not make…

We study the behavior of infinite systems of coupled harmonic oscillators as t->infinity, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This…

We show that the variance of centred linear statistics of eigenvalues of GUE matrices remains bounded for large $n$ for some classes of test functions less regular than Lipschitz functions. This observation is suggested by the limiting form…

This article constructs simultaneous confidence bands (SCBs) for functional parameters using the Gaussian Kinematic formula of $t$-processes (tGKF). Although the tGKF relies on Gaussianity, we show that a central limit theorem (CLT) for the…

We introduce a framework to derive quantitative central limit theorems in the context of non-linear approximation of Gaussian random variables taking values in a separable Hilbert space. In particular, our method provides an alternative to…