加权伯努利和的Rényi熵的乘法比较
Multiplicative comparisons of Rényi entropies for weighted Bernoulli sums
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中文总结 AI 辅助
该研究针对独立伯努利随机变量加权和，改进了不同阶Rényi熵的乘法比较界，获得零阶与无穷阶间的对数界及非零阶间的显式常数因子界，实现了对已有结果的多项式改进。
中文摘要 AI 辅助
我们建立了独立伯努利随机变量加权和的不同阶Rényi熵之间的改进乘法界。特别地，我们证明了零阶与无穷阶Rényi熵之间的对数界，这相比Jain、Sah和Sawhney的平方根界实现了多项式级改进。此外，我们得到了非零阶Rényi熵之间比较的显式常数因子界。
英文摘要
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.
