Bernoulli sums and Rényi entropy inequalities

Abstract

We investigate the Rényi entropy of independent sums of integer valued random variables through Fourier theoretic means, and give sharp comparisons between the variance and the Rényi 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''.

References in corpus (6)

• Dimensional behaviour of entropy and information
• Transport-majorization to analytic and geometric inequalities
• Volumes of subset Minkowski sums and the Lyusternik region
• Log-concave poset inequalities
• Concentration inequalities for log-concave sequences
• Erdos-Littlewood-Offord problem with arbitrary probabilities

Cited by in corpus (2)

• Transport-majorization to analytic and geometric inequalities
• Entropy-variance inequalities for discrete log-concave random variables via degree of freedom