Related papers: Central Limit Theorems on Compact Metric Spaces

In the present paper, we study central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering graphs from a point of view of discrete geometric analysis developed by Kotani and Sunada. We establish a semigroup CLT for a…

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…

Fr\'echet mean and variance provide a way of obtaining mean and variance for general metric space valued random variables and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and…

Statistical inferences for sample correlation matrices are important in high dimensional data analysis. Motivated by this, this paper establishes a new central limit theorem (CLT) for a linear spectral statistic (LSS) of high dimensional…

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…

Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…

We establish finite-sample error bounds in expectation for transformed Fr\'echet means in Hadamard spaces under minimal assumptions. Transformed Fr\'echet means provide a unifying framework encompassing classical and robust notions of…

We establish a quenched Central Limit Theorem (CLT) for a smooth observable of random sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an annealed CLT for the same system. We show that, almost surely,…

We prove annealed central limit theorems for finite pattern counts in the measurement record of discrete-time quantum trajectories generated by repeated measurements in a disordered environment. Under summable mixing assumptions on the…

We study some sufficient conditions imposed on the sequence of martingale differences (m.d.) in the separable Banach spaces of continuous functions defined on the metric compact set for the Central Limit Theorem in this space. We taking…

Let $\{u(t,x)\}_{t>0,x\in{{\mathbb R}^{d}}}$ denote the solution to a $d$-dimensional parabolic Anderson model with delta initial condition and driven by a multiplicative noise that is white in time and has a spatially homogeneous…

The question of whether the central limit theorem (CLT) holds for the total number of edges in exponential random graph models (ERGMs) in the subcritical region of parameters has remained an open problem. In this paper, we establish the…

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…

We establish central limit theorems (CLTs) for the linear spectral statistics of the adjacency matrix of inhomogeneous random graphs across all sparsity regimes, providing explicit covariance formulas under the assumption that the variance…

We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bounds for convergence in transportation distance and entropy,…

We show how the renormalization group approach can be used to prove quantitative central limit theorems (CLTs) in the setting of free, Boolean, bi-free and bi-Boolean independence under finite third moment assumptions. The proofs rely on…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

When the underlying random variables are Gaussian, the classical Central Limit Theorem (CLT) is trivial, but the functional CLT is not. The objective of the paper is to investigate the functional CLT for stationary Gaussian processes in the…

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…

We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or $\beta$-ensembles. We use a method based on a change of variables which allows to treat fairly general situations, including multi-cut and, for the…