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Sharp Metric Xp Inequalities via Martingales
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 Xp inequality for Lp, resolving an open question posed by Naor.
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BibTeX
@misc{areshidze2026sharp,
title = {{Sharp Metric $X_p$ Inequalities via Martingales}},
author = {Nika Areshidze},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.29367},
eprint = {2608.29367},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29367},
}
RIS
TY - UNPB
TI - Sharp Metric X_p Inequalities via Martingales
AU - Nika Areshidze
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2608.29367
UR - https://arxiv.org/abs/2608.29367
AB - 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.
ER -