Related papers: An information-theoretic Central Limit Theorem for…
We adapt arguments concerning information-theoretic convergence in the Central Limit Theorem to the case of dependent random variables under Rosenblatt mixing conditions. The key is to work with random variables perturbed by the addition of…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…
We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method,…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…
This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…
In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated. Several limit theorems are established:…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy…
In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study…
Fluctuation theorems and the second law of thermodynamics are powerful relations constraining the behavior of out-of-equilibrium systems. While there exist generalizations of these relations to feedback controlled quantum systems, their…
According to the universal entropy bound, the entropy (and hence information capacity) of a complete weakly self-gravitating physical system can be bounded exclusively in terms of its circumscribing radius and total gravitating energy. The…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
We study the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. The minimum entropy required for such a latent is known as common entropy in information theory. We…
This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
The paper deals with conditional linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid…
A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a…