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Entropy-variance inequalities for discrete log-concave random variables via degree of freedom

Heshan Aravinda
Dec 2022
摘要
We utilize a discrete version of the notion of degree of freedom to prove asharp min-entropy-variance inequality for integer valued log-concave randomvariables. More specifically, we show that the geometric distribution minimizesthe min-entropy within the class of log-concave probability sequences withfixed variance. As an application, we obtain a discrete R\'enyi entropy powerinequality in the log-concave case, which improves a result of Bobkov,Marsiglietti and Melbourne (2022).
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