Entropy Inequalities for Sums in Prime Cyclic Groups
نویسندگان
چکیده
Lower bounds for the Rényi entropies of sums of independent random variables taking values in cyclic groups of prime order, or in the integers, 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.
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عنوان ژورنال:
- CoRR
دوره abs/1710.00812 شماره
صفحات -
تاریخ انتشار 2017