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arXiv · 2409.03664

The Kneser--Poulsen phenomena for entropy

Gautam Aishwarya·Dongbin Li
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Abstract

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 R\'enyi entropy comparisons between a probability measure and its contractive image are preserved when both undergo simultaneous heat flow. An inequality that unifies Costa's result on the concavity of entropy power with the entropic Kneser--Poulsen theorem is also presented.

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Gautam Aishwarya, Dongbin Li. 2024-09-05. The Kneser--Poulsen phenomena for entropy. https://arxiv.org/abs/2409.03664

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