Related papers: Central limit theorems for Fr\'echet means on stra…

We obtain a functional central limit theorem (CLT) for sums of the form $\xi_N(t)=\frac1{\sqrt N}\sum_{n=1}^{[Nt]}\big(F(X(q_1(n)),...,X(q_\ell(n)))-\bar F\big)$ where $q_1,...,q_\ell$ are polynomials.

We investigate the dependence of the center-of-mass tomogram of a system with many degrees of freedom $N$ on the Planck constant $\hbar $. It is shown that to use the central limit theorem under taking the limit $N\to +\infty $ one should…

We study linear spectral statistics of high dimensional sample covariance matrices in a regime where the empirical spectral distribution remains governed by the classical sample covariance law but the fluctuation theory is nonclassical. Our…

Let $G$ be a group with a non-elementary action on a proper CAT(0) space $X$, and let $\mu$ be a measure on $G$ such that the random walk $(Z_n)_n$ generated by $\mu$ has finite second moment on $X$. Let $o$ be a basepoint in $X$, and…

We prove central limit theorems (CLTs) for topological functionals of Bernoulli bond percolation on infinite graphs beyond the Euclidean lattice $\mathbb{Z}^{d}$. For quasi-transitive graphs of subexponential growth, we show that the number…

Fr\'echet means on non-Euclidean spaces may exhibit nonstandard asymptotic rates rendering quantile-based asymptotic inference inapplicable. We show here that this affects, among others, all circular distributions whose support exceeds a…

Consider a $N\times n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are given by $$ Y_{ij}^{n}=\frac{\sigma_{ij}(n)}{\sqrt{n}} X_{ij}^{n} $$ the $X_{ij}^{n}$ being centered, independent and identically distributed random variables…

In this paper, we derive a unified method for establishing the distributional convergence of linear eigenvalue statistics (LES) for generalized patterned random matrices. We prove that for an $N \times N$ generalized patterned random matrix…

Establishing central limit theorems (CLTs) for ergodic averages of Markov chains is a fundamental problem in probability and its applications. Since the seminal work~\cite{MR834478}, a vast literature has emerged on the sufficient…

We consider the Laguerre Unitary Ensemble (LUE), the set of $n\times n$ sample covariance matrices $M = \frac{1}{n}X^*X$ where the $m\times n$ ($n \le m$) matrix $X$ has i.i.d. standard complex Gaussian entries. In particular we are…

We consider the hard-edge scaling of the Mittag-Leffler ensemble confined to a fixed disk inside the droplet. Our primary emphasis is on fluctuations of rotationally-invariant additive statistics that depend on the radius and thus give rise…

We prove central limit theorems for the random walks on either the mapping class group of a closed, connected, orientable, hyperbolic surface, or on $\text{Out}(F_N)$, each time under a finite second moment condition on the measure (either…

Le Cam's third/contiguity lemma is a fundamental probabilistic tool to compute the limiting distribution of a given statistic $T_n$ under a non-null sequence of probability measures $\{Q_n\}$, provided its limiting distribution under a null…

We consider first-passage percolation on $\mathbb{Z}^2$ with i.i.d. weights, whose distribution function satisfies $F(0) = p_c = 1/2$. This is sometimes known as the "critical case" because large clusters of zero-weight edges force passage…

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…

Estimating the mean of a random vector from i.i.d. data has received considerable attention, and the optimal accuracy one may achieve with a given confidence is fairly well understood by now. When the data take values in more general metric…

In this paper, we establish the convergence rate in central limit theorem (CLT) for linearly extended negative quadrant dependent (LENQD) random variables (rv's). Under some weak conditions, the rate of normal approximation is shown as…

In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative…

We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We extend results in [19] and prove asymptotic stability of both optimal transport…

Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given…