Rényi entropy and variance comparison for symmetric log-concave random variables

08/23/2021

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by   Maciej Białobrzeski, et al.

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We show that for any α>0 the Rényi entropy of order α is minimized, among all symmetric log-concave random variables with fixed variance, either for a uniform distribution or for a two sided exponential distribution. The first case occurs for α∈ (0,α^*] and the second case for α∈ [α^*,∞), where α^* satisfies the equation 1/α^*-1logα^*= 1/2log 6, that is α^* ≈ 1.241.