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Some entropy properties of discrete random variables

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MQIW05 - Beyond I.I.D. in information theory

It is well-known that Gaussian random variables have many attractive properties: they are maximum entropy, they are stable under addition and scaling, they give equality in the Entropy Power Inequality (and hence give sharp log-Sobolev inequalities) and have good entropy concavity properties. I will discuss the extent to which results of this kind can be formulated for discrete random variables, and how they relate to ideas of discrete log-concavity.




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