Related papers: A Proof of a Non-Commutative Central Limit Theorem…

Let $\alpha$ be a Steinhaus or a Rademacher random multiplicative function. For a wide class of multiplicative functions $f$ we show that the sum $\sum_{n \le x}\alpha(n) f(n)$, normalised to have mean square $1$, has a non-Gaussian…

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…

We adapt arguments concerning information-theoretic convergence in the Central Limit Theorem to the case of dependent random variables under Rosenblatt mixing conditions. The key is to work with random variables perturbed by the addition of…

We prove the Central Limit Theorem for linear statistics of the eigenvalues of band random matrices provided $\sqrt{n} \ll b_n \ll n$ and test functions are sufficiently smooth.

Our purpose is to prove central limit theorem for countable nonhomogeneous Markov chain under the condition of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chain in Ces\`aro sense. Furthermore,…

We interpret the Central Limit Theorem as a fixed point theorem for a certain operator, and consider the problem of linearizing this operator. In classical as well as in free probability theory, we consider two methods giving such a…

In this paper, we provide a central limit theorem for the finite-dimensional marginal distributions of empirical processes $(Z_n(f))_{f\in\mathcal{F}}$ whose index set $\mathcal{F}$ is a family of cluster functionals valued on blocks of…

Bringing forward the concept of convergence in moments from classical random variables to quantum random variables is what leads to what can be called algebraic central limit theorem for (classical and) quantum random variables. I reflect…

We establish self-norming central limit theorems for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations are obtained by perturbing the slope in the…

This paper aims to establish a central limit theorem for Markov processes conditioned not to be absorbed under a very general assumption on quasi-stationarity for the underlying process. To do so, a central limit theorem has been…

We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…

We prove a variant of the central limit theorem (CLT) for a sequence of i.i.d. random variables $\xi_j$, perturbed by a stochastic sequence of linear transformations $A_j$, representing the model uncertainty. The limit, corresponding to a…

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…

This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study…

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly…

We establish a central limit theorem (CLT) for families of products of $\epsilon$-independent random variables. We utilize graphon limits to encode the evolution of independence and characterize the limiting distribution. Our framework…

We describe a proof of the Central Limit Theorem that has been formally verified in the Isabelle proof assistant. Our formalization builds upon and extends Isabelle's libraries for analysis and measure-theoretic probability. The proof of…

In this paper we consider a sequence of random variables with mean uncertainty in a sublinear expectation space. Without the hypothesis of identical distributions, we show a new central limit theorem under the sublinear expectations.

In this article, we establish a central limit theorem for the capacity of the range process for a class of $d$-dimensional symmetric $\alpha$-stable random walks with the index satisfying $d > 5\alpha /2$. Our approach is based on…

In this paper we show a central limit theorem for Lebesgue integrals of stationary $BL(\theta)$-dependent random fields as the integration domain grows in Van Hove-sense. Our method is to use the (known) analogue result for discrete sums.…