Quantitative form of Ball's Cube slicing in ℝⁿ and equality cases in the min-entropy power inequality

2021/09/08 by Melbourne, James, Roberto, Cyril
#FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2109.03946

Abstract

We prove a quantitative form of the celebrated Ball's theorem on cube slicing in ℝⁿ and obtain, as a consequence, equality cases in the min-entropy power inequality. Independently, we also give a quantitative form of Khintchine's inequality in the special case p=1.

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