The Kneser--Poulsen phenomena for entropy
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915387130511360 |
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| author | Aishwarya, Gautam Li, Dongbin |
| author_facet | Aishwarya, Gautam Li, Dongbin |
| contents | 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. An inequality that unifies Costa's result on the concavity of entropy power with the entropic Kneser--Poulsen theorem is also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Kneser--Poulsen phenomena for entropy Aishwarya, Gautam Li, Dongbin Metric Geometry Information Theory Probability 37C10, 94A17, 52A40, 52A20 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. An inequality that unifies Costa's result on the concavity of entropy power with the entropic Kneser--Poulsen theorem is also presented. |
| title | The Kneser--Poulsen phenomena for entropy |
| topic | Metric Geometry Information Theory Probability 37C10, 94A17, 52A40, 52A20 |
| url | https://arxiv.org/abs/2409.03664 |