Entropic exercises around the Kneser-Poulsen conjecture

Abstract

We develop an information-theoretic approach to study the Kneser--Poulsen conjecture in discrete geometry. This leads us to a broad question regarding whether Rényi entropies of independent sums decrease when one of the summands is contracted by a $1$-Lipschitz map. We answer this question affirmatively in various cases.

23 pages, comments welcome! Final version with minor changes, added Corollary 2.8 (linear contractions decrease intrinsic volumes of convex bodies)