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arXiv · 2608.29367

Sharp Metric $X_p$ Inequalities via Martingales

Nika Areshidze
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Abstract

We prove a sharp higher-order Rademacher-chaos inequality on the Hamming cube using random-reveal martingales. As a consequence, we obtain the sharp metric $X_p$ inequality for $L^p$, resolving an open question posed by Naor.

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Nika Areshidze. 2026-08-29. Sharp Metric $X_p$ Inequalities via Martingales. https://arxiv.org/abs/2608.29367

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