Multiplicative comparisons of Rényi entropies for weighted Bernoulli sums

2026-09-01

AI Summary

本文通过改进的乘法界解决了不同阶Rényi熵之间的关系问题，特别是对于加权伯努利随机变量和，提供了一个对数界。

Abstract

We establish improved multiplicative bounds relating the Rényi entropies of different orders for weighted sums of independent Bernoulli random variables. In particular, we prove a logarithmic bound between the zeroth-order and infinity-order Rényi entropies, which yields a polynomial improvement over the square-root bound of Jain, Sah, and Sawhney. Additionally, we obtain explicit constant-factor bounds for comparisons among Rényi entropies of nonzero orders.

Problem

• Rényi entropies
• weighted Bernoulli sums
• multiplicative bounds

Innovation

• Rényi entropies
• weighted Bernoulli sums
• multiplicative bounds
• logarithmic bound
• constant-factor bounds