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Abstract. A generalization of Young’s inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges. The conjecture would provide a unified proof of recent entropy power inequalities of Barron and Madiman, as well as of a (conjectured)(More)
A lower bound on the Rényi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the entropy power inequality. Several applications are discussed, including a new proof of the classical entropy power(More)
A new lower bound on the entropy of the sum of independent random vectors is demonstrated in terms of rearrangements. This lower bound is better than that given by the entropy power inequality. In fact, we use it to give a new, independent, and simple proof of the entropy power inequality in the case when the summands are identically distributed. We also(More)
An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean. These bounds significantly improve on the bounds obtained by Bobkov and Madiman (Ann. Probab., 39(4):1528–1543, 2011). Mathematics Subject Classification (2010). Primary 52A40;(More)
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,(More)
There is an urgent need to develop scalable approaches to community-based mental health services for children in rural China and other developing countries involving task shifting from clinicians to trained community workers. Evidence is needed about the effectiveness of interventions for children affected by AIDS in rural areas. This article describes an(More)
A simple new lower bound is provided for the Rényi entropy of the convolution of probability distributions on the integers in terms of certain (discrete) rearrangements of these distributions. This inequality may be thought of as an entropy power inequality for integer-valued random variables.
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