Entropic exercises around the Kneser-Poulsen conjecture

Autor:	Aishwarya, Gautam, Alam, Irfan, Li, Dongbin, Myroshnychenko, Sergii, Zatarain-Vera, Oscar
Rok vydání:	2022
Předmět:	Mathematics - Metric Geometry Computer Science - Information Theory Mathematics - Probability 52A38 52A20 52A40 94A17
Zdroj:	Mathematika, Volume 69, Issue 3, pp. 841-866 (2023)
Druh dokumentu:	Working Paper
DOI:	10.1112/mtk.12210
Popis:	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. Comment: 23 pages, comments welcome! Final version with minor changes, added Corollary 2.8 (linear contractions decrease intrinsic volumes of convex bodies)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.12842 Zobrazit plný text záznamu View this record from Arxiv