Minkowski summation is a basic and ubiquitous operation on sets. Indeed, the Minkowski
sum ACBD fa C b W a 2 A; b 2 Bg of sets A and B makes sense as long as A and B are …

The entropy power inequality, which plays a fundamental role in information theory and
probability, may be seen as an analogue of the Brunn-Minkowski inequality. Motivated by …

A lower bound on the Rényi differential entropy of a sum of independent random vectors is
demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon …

This paper gives improved Rényi entropy power inequalities (R-EPIs). Consider a sum S n=
Σ k= 1 n X k of n independent continuous random vectors taking values on ℝ d, and let …

The fundamental limits of remote estimation of autoregressive Markov processes under
communication constraints are presented. The remote estimation system consists of a …

Over the past few years, a family of interesting new inequalities for the entropies of sums and
differences of random variables has been developed by Ruzsa, Tao, and others, motivated …

General extensions of an inequality due to Rogozin, concerning the essential supremum of
a convolution of probability density functions on the real line, are obtained. While a weak …

We initiate the study of the Stam region, defined as the subset of the positive orthant in ℝ (2
n-1) that arises from considering the entropy powers of subset sums of n independent …

We begin a systematic study of the region of possible values of the volumes of Minkowski
subset sums of a collection of M compact sets in R d, which we call the Lyusternik region …

Lower bounds for the Rényi entropies of sums of independent random variables taking
values in cyclic groups of prime order under permutations are established. The main …