The Kneser--Poulsen phenomena for entropy

The Kneser--Poulsen conjecture asserts that the volume of a union of balls in Euclidean space cannot be increased by bringing their centres pairwise closer. We prove that its natural information-theoretic counterpart is true. This follows from a complete answer to a question asked in arXiv:2210.1284...

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Bibliographic Details
Published inarXiv.org
Main Authors Gautam Aishwarya, Li, Dongbin
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.09.2024
Subjects
Entropy (Information theory)
Euclidean geometry
Heat transmission
Information theory
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Summary:The Kneser--Poulsen conjecture asserts that the volume of a union of balls in Euclidean space cannot be increased by bringing their centres pairwise closer. We prove that its natural information-theoretic counterpart is true. This follows from a complete answer to a question asked in arXiv:2210.12842 about Gaussian convolutions, namely that the Rényi entropy comparisons between a probability measure and its contractive image are preserved when both undergo simultaneous heat flow.
ISSN:2331-8422