Entropy, central limit theorem and related problems - Talk 2. Entropy power inequality for Renyi entropy

Abstract. A basic theme for these talks will be the behaviour of the (differential) entropy on convolutions. First, we discuss general properties of the entropy functional, including the entropy power inequality. Renyi's entropy is a natural generalization which shares a number of similar properies. Then we will turn to the problem of rates of convergence in the entropic central limit theorem, and will discuss its connections with the CLT for transport metrics.