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 R\'enyi 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.
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