The Kneser--Poulsen phenomena for entropy
<|reference_start|>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:2210.12842 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.<|reference_end|>
@article{aishwarya2024the,
    title={The Kneser--Poulsen phenomena for entropy},
    author={Gautam Aishwarya, Dongbin Li},
    journal={arXiv preprint arXiv:2409.03664},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.03664},
    primaryClass={math.MG cs.IT math.IT math.PR}
}