Related papers: Uniform limit theorems under random truncation

In this paper we consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in $\Rd$ and undergoing a binary, supercritical branching with a constant rate $\lambda>0$. This system is…

We prove a law of large numbers and a central limit theorem for a tagged particle in a symmetric simple exclusion process in the one-dimensional lattice with variable diffusion coefficient. The scaling limits are obtained from a similar…

We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails…

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…

Large Language Models (LLMs) have demonstrated remarkable capabilities, yet their scalability raises a critical question: Have we reached the scaling ceiling? This paper addresses this pivotal question by developing a unified theoretical…

This paper re-examines the limit theorems of Abadie and Imbens for nearest-neighbor matching estimators of average treatment effects with a fixed number of matches. We establish, for the first time, a non-normalized central limit theorem…

The paper consists of two parts. In the first part we review recent work on limit theorems for random walks in random environment (RWRE) on a strip with jumps to the nearest layers. In the second part, we prove the quenched Local Limit…

Motivated by random evolutions which do not start from equilibrium, in a recent work, Peligrad and Voln\'{y} (2018) showed that the quenched CLT (central limit theorem) holds for ortho-martingale random fields. In this paper, we study the…

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…

Suppose $B_i:= B(p,r_i)$ are nested balls of radius $r_i$ about a point $p$ in a dynamical system $(T,X,\mu)$. The question of whether $T^i x\in B_i$ infinitely often (i. o.) for $\mu$ a.e.\ $x$ is often called the shrinking target problem.…

A central limit theorem (CLT) for the smoothed empirical spectral distribution of sample covariance matrices is established. Moreover, the CLTs for the smoothed quantiles of Marcenko and Pastur's law have been also developed.

This paper provides a Central Limit Theorem (CLT) for a process $\{\theta_n, n\geq 0\}$ satisfying a stochastic approximation (SA) equation of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H(\theta_n,X_{n+1})$; a CLT for the associated…

In this paper, we establish the central limit theorem (CLT) for the linear spectral statistics (LSS) of sample correlation matrix $R$, constructed from a $p\times n$ data matrix $X$ with independent and identically distributed (i.i.d.)…

This paper establishes a combinatorial central limit theorem for stratified randomization, which holds under a Lindeberg-type condition. The theorem allows for an arbitrary number or sizes of strata, with the sole requirement being that…

We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a…

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…

We prove CLTs for biased randomly trapped random walks in one dimension. In particular, we will establish an annealed invariance principal by considering a sequence of regeneration times under the assumption that the trapping times have…

Let (Z n) n$\ge$0 with Z n = (Z n (i, j)) 1$\le$i,j$\le$p be a p multi-type critical branching process in random environment, and let M n be the expectation of Z n given a fixed environment. We prove theorems on convergence in distribution…

We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$, in the limit of large $n$. Since in unconstrained uniform random permutations most of the indices are in cycles of…

We use a multivariate central limit theorem (CLT) to study the distribution of random geometric graphs (RGGs) on the cube and torus in the high-dimensional limit with general node distributions. We find that the distribution of RGGs on the…