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Multiplicative comparisons of Rényi entropies for weighted Bernoulli sums

  • Jiange Li
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Abstract

We establish multiplicative comparisons between Rényi entropies of different orders for weighted sums of independent Bernoulli random variables. In particular, we prove a logarithmic comparison between the zeroth- and infinity-order Rényi entropies, which yields a polynomial improvement over the square-root bound of Jain, Sah, and Sawhney. As an application, this leads to an improved parameterized running time for the randomized bin-packing algorithm of Nederlof, Pawlewicz, Swennenhuis, and Wȩgrzycki. We also obtain explicit dimension-free, constant-factor comparisons between Rényi entropies of positive orders.

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Cite

BibTeXRIS
BibTeX
@misc{li2026multiplicative,
  title = {{Multiplicative comparisons of Rényi entropies for weighted Bernoulli sums}},
  author = {Jiange Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01529},
  eprint = {2609.01529},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01529},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Multiplicative comparisons of Rényi entropies for weighted Bernoulli sums
AU  - Jiange Li
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.01529
UR  - https://arxiv.org/abs/2609.01529
AB  - We establish multiplicative comparisons between Rényi entropies of different orders for weighted sums of independent Bernoulli random variables. In particular, we prove a logarithmic comparison between the zeroth- and infinity-order Rényi entropies, which yields a polynomial improvement over the square-root bound of Jain, Sah, and Sawhney. As an application, this leads to an improved parameterized running time for the randomized bin-packing algorithm of Nederlof, Pawlewicz, Swennenhuis, and Wȩgrzycki. We also obtain explicit dimension-free, constant-factor comparisons between Rényi entropies of positive orders.
ER  -