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arXiv · 2210.12842

Entropic exercises around the Kneser-Poulsen conjecture

Gautam Aishwarya·Irfan Alam·Dongbin Li·Sergii Myroshnychenko·Oscar Zatarain-Vera
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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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Gautam Aishwarya, Irfan Alam, Dongbin Li, Sergii Myroshnychenko, Oscar Zatarain-Vera. 2022-10-23. Entropic exercises around the Kneser-Poulsen conjecture. https://doi.org/10.1112/mtk.12210

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