We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree of log-concavity. Along the way, we recover, improve, and simplify several results existing in the literature. Our approach is based on majorization in the convex order.

翻译：我们通过概率解释探究对数凹性概念的定量含义。特别地，我们推导了满足精确对数凹度随机变量的集中不等式、矩与熵界。在此过程中，我们恢复、改进并简化了文献中已有的若干结果。我们的方法基于凸序下的优化理论。