Minimum entropy of a log-concave variable for fixed variance

09/04/2023

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by   James Melbourne, et al.

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We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable. We apply this result to derive upper bounds on capacities of additive noise channels with log-concave noise. We also improve constants in the reverse entropy power inequalities for log-concave random variables.