Certain Relations in Statistical Physics Based on Rényi Entropy

Statistical Inference for Rényi Entropy Functionals

Numerous entropy-type characteristics (functionals) generalizing Rényi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and distribution identification problems. We consider estimators of some entropy (integral) functionals for discrete and continuous distributions based on the numb...

Lectures on Probability, Entropy, and Statistical Physics

Preface Science consists in using information about the world for the purpose of predicting , explaining, understanding, and/or controlling phenomena of interest. The basic difficulty is that the available information is usually insufficient to attain any of those goals with certainty. In these lectures we will be concerned with the problem of inductive inference , that is, the problem of reaso...

On the Conditional Rényi Entropy

On Rényi entropy power inequalities

This paper is a follow-up of a recent work by Bobkov and Chistyakov, obtaining some improved Rényi entropy power inequalities (R-EPIs) for sums of independent random vectors. The first improvement relies on the same bounding techniques used in the former work, while the second significant improvement relies on additional interesting properties from matrix theory. The improvements obtained by th...

Smooth Entropy and Rényi Entropy

The notion of smooth entropy allows a unifying, generalized formulation of privacy ampli-cation and entropy smoothing. Smooth entropy is a measure for the number of almost uniform random bits that can be extracted from a random source by probabilistic algorithms. It is known that the R enyi entropy of order at least 2 of a random variable is a lower bound for its smooth entropy. On the other ha...