Entropic exercises around the Kneser–Poulsen conjecture

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2023-06-06 DOI:10.1112/mtk.12210

Gautam Aishwarya, Irfan Alam, Dongbin Li, Sergii Myroshnychenko, Oscar Zatarain-Vera

引用次数: 0

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.

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Kneer–Poulsen猜想的熵练习

我们开发了一种信息论方法来研究离散几何中的Kneer–Poulsen猜想。这就引出了一个广泛的问题，即当其中一个和被1‐Lipschitz映射收缩时，独立和的Rényi熵是否会减小。我们在各种情况下都肯定地回答了这个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.