Related papers: Corrections to the Central Limit Theorem for Heavy…
Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…
This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…
We consider point particle that collides with a periodic array of hard-core elastic scatterers where the length of the free flights is unbounded (the infinite-horizon Lorentz gas, LG). The Bleher central limit theorem (CLT) states that the…
We consider the existence of the integrated density of states (IDS) of the Anderson model on the Hilbert space $\ell^2(\mathbb{Z}^d)$ as analogues to the law of large numbers (LLN). In this work, we prove the analogues central limit theorem…
A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…
We develop a higher-order asymptotic analysis for the semi-hard triplet loss using the Edgeworth expansion. It is known that this loss function enforces that embeddings of similar samples are close while those of dissimilar samples are…
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…
Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…
We develop Edgeworth expansion theory for spot volatility estimator under general assumptions on the log-price process that allow for drift and leverage effect. The result is based on further estimation of skewness and kurtosis, when…
High dimensional central limit theorems (the CLTs) have been extensively studied in recent years under a variety of sufficient moment conditions connecting the dimension growth rate with the tail decay rate. In this article, we investigate…
The problem of sums of independent, identically distributed random variables with stretched-exponential tails exhibits a dynamical phase transition and has recently reemerged in the context of active transport and condensation phenomena. We…
We study the distribution of a general class of asymptoticallylinear statistics which are symmetric functions of $N$ independent observations. The distribution functions of these statistics are approximated by an Edgeworth expansion with a…
We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all…
We study the Central Limit Theorem (CLT) in the so-called mixed (anisotropic) Lebesgue-Riesz spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.
We show that there exists a very natural, superstatistics-linked extension of the central limit theorem (CLT) to deformed exponentials (also called q-Gaussians): This generalization favorably compares with the one provided by S. Umarov and…
We study asymptotic expansions in free probability. In a class of classical limit theorems Edgeworth expansion can be obtained via a general approach using sequences of "influence" functions of individual random elements described by…
We prove a central limit theorem (CLT) for the number of joint orbits of random tuples of commuting permutations. In the uniform sampling case this generalizes the classic CLT of Goncharov for the number of cycles of a single random…
We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random…
In this note, we assess the accuracy of CLT-based approximations for the volume of intersection of the $d$-dimensional cube $[-1,1]^d$ and an $L_q$-ball centred at the origin; this is clearly equivalent to approximating the distribution of…
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…