Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Li, Jiange
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206205017