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arXiv · 2505.00944

From simplex slicing to sharp reverse H\"older inequalities

James Melbourne·Michael Roysdon·Colin Tang·Tomasz Tkocz
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Abstract

Simplex slicing (Webb, 1996) is a sharp upper bound on the volume of central hyperplane sections of the regular simplex. We extend this to sharp bounds in the probabilistic framework of negative moments, and beyond, of centred log-concave random variables, establishing a curious phase transition of the extremising distribution for new sharp reverse H\"older-type inequalities.

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James Melbourne, Michael Roysdon, Colin Tang, Tomasz Tkocz. 2025-05-02. From simplex slicing to sharp reverse H\"older inequalities. https://arxiv.org/abs/2505.00944

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