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Theoretical analysis reveals sharp lower bounds on p-norms and Rényi entropy for sums of uniform random variables, establishing optimal variance-based inequalities.
We provide a sharp lower bound on the p-norm of a sum of independent uniform random variables in terms of its variance when $0 < p < 1$. We address an analogous question for p-Rényi entropy for p in the same range.
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Chasapis et al. (2021) studied this question.
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