论文标题
通过自由程度的离散对数符号随机变量的熵变化不平等现象
Entropy-variance inequalities for discrete log-concave random variables via degree of freedom
论文作者
论文摘要
我们利用自由度概念的离散版本来证明整数有价值的对数符合随机变量的尖锐的最小内整形变化不平等。更具体地说，我们表明几何分布最大程度地减少了具有固定方差的对数符合概率序列中的最小渗透。作为应用程序，我们在对数洞穴案例中获得了离散的Rényi熵功率不平等，该案例改善了Bobkov，Marsiglietti和Melbourne（2022）的结果。
We utilize a discrete version of the notion of degree of freedom to prove a sharp min-entropy-variance inequality for integer valued log-concave random variables. More specifically, we show that the geometric distribution minimizes the min-entropy within the class of log-concave probability sequences with fixed variance. As an application, we obtain a discrete Rényi entropy power inequality in the log-concave case, which improves a result of Bobkov, Marsiglietti and Melbourne (2022).
