Related papers: Central limit theorems for nonlinear hierarchical …

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

Here we obtain the exact asymptotics for large and moderate deviations, strong law of large numbers and central limit theorem for chains with unbounded variable length memory.

Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…

We study the limiting behavior for the solutions of a nonlinear recurrent relation which arises from the study of Navier-Stokes equations. Some stability theorems are also shown concerning a related class of linear recurrent relations.

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…

We prove the annealed Central Limit Theorem for random walks in bistochastic random environments on $Z^d$ with zero local drift. The proof is based on a "dynamicist's interpretation" of the system, and requires a much weaker condition than…

We establish a central limit theorem for tensor product random variables $c_k:=a_k \otimes a_k$, where $(a_k)_{k \in \mathbb{N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the…

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…

The divergence of the thermal conductivity in the thermodynamic limit is thoroughly investigated. The divergence law is consistently determined with two different numerical approaches based on equilibrium and non-equilibrium simulations. A…

We show how a central limit theorem for Poisson model random polygons implies a central limit theorem for uniform model random polygons. To prove this implication, it suffices to show that in the two models, the variables in question have…

In this paper we will prove a functional central limit theorems for "nonconventional" sums indexed by polynomial arrays.

We obtain large deviations estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems (CLT) obtained by Nicol,…

A new sufficient condition is proposed in the problem of Central Limit Theorem in the array scheme for non-homogeneous Markov Chains.

We prove a central limit theorem for the volume of projections of the N-cube onto a random subspace of dimension n, when n is fixed and N tends to infinity. Randomness in this case is with respect to the Haar measure on the Grassmannian…

We consider a borderline case: the central limit theorem for a strictly stationary time series with infinite variance but a Gaussian limit. In the iid case a well-known sufficient condition for this central limit theorem is regular…

We study fluctuations of linear statistics corresponding to smooth functions for certain biorthogonal ensembles. We study those biorthogonal ensembles for which the underlying biorthogonal family satisfies a finite term recurrence and…

In this paper is proved the limit theorem for randomly indexed sequence of random processes in the case where sequences of random index and random processes are independent, also the estimation of convergence rate is obtained.

Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…

As generalizations of random graphs, random simplicial complexes have been receiving growing attention in the literature. In this paper, we naturally extend the Random Connection Model (RCM), a random graph that has been extensively studied…