Reversal of Rényi Entropy Inequalities Under Log-Concavity
James Melbourne, Tomasz Tkocz
Abstract
We establish a discrete analog of the Rényi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within log e of the usual Shannon entropy. Additionally we investigate the entropic Rogers-Shephard inequality studied by Madiman and Kontoyannis, and establish a sharp Rényi version for certain parameters in both the continuous and discrete cases.
Topics & Concepts
MathematicsRényi entropyEntropy (arrow of time)Entropy power inequalityInformation theoryStatistical physicsMin entropyCombinatoricsMaximum entropy probability distributionDiscrete mathematicsMaximum entropy thermodynamicsJoint quantum entropyPrinciple of maximum entropyStatisticsPhysicsThermodynamicsLimits and Structures in Graph TheoryMarkov Chains and Monte Carlo MethodsWireless Communication Security Techniques