Lower bounds for the R\'enyi entropies of sums of independent random variables taking values in cyclic groups of prime order under permutations are established. The main ingredients of our approach are extended rearrangement inequalities in prime cyclic groups building on Lev (2001), and notions of stochastic ordering. Several applications are developed, including to discrete entropy power inequalities, the Littlewood-Offord problem, and counting solutions of certain linear systems.

翻译：R\'enyi 的下边界限是独立随机变量总和的下边界限,这些变量的数值取自在变异状态下按基本秩序的周期组的数值,我们的方法的主要内容是:在列夫(2001年)的基础上扩大主要周期组的重新排列不平等,以及随机定购的概念。 我们开发了几种应用,包括离散的环形电源不平等、小伍德-福福德问题,以及某些线性系统的计数解决方案。