We investigate the R\'enyi entropy of independent sums of integer valued random variables through Fourier theoretic means, and give sharp comparisons between the variance and the R\'enyi entropy, for Poisson-Bernoulli variables. As applications we prove that a discrete ``min-entropy power'' is super additive on independent variables up to a universal constant, and give new bounds on an entropic generalization of the Littlewood-Offord problem that are sharp in the ``Poisson regime''.

翻译：我们通过傅里叶理论方法研究整数值随机变量独立和的Rényi熵，并给出泊松-伯努利变量在方差与Rényi熵之间的精确比较。作为应用，我们证明离散“最小熵幂”在独立变量上具有超可加性（至多相差一个普适常数），并为Littlewood-Offord问题的熵推广形式给出新界，该界在“泊松区域”达到最优。