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Szarek and Ball made simple
Abstract
We present proofs of Szarek's moment comparison and Ball's cube slicing inequalities based on elementary convexity and majorisation. The key ingredient is a moment-lifting argument which allows us to use Schur monotonicity, avoiding the integral inequalities used in the original Fourier-analytic approaches.
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BibTeX
@misc{tang2026szarek,
title = {{Szarek and Ball made simple}},
author = {Colin Tang and Tomasz Tkocz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28384},
eprint = {2610.28384},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28384},
}
RIS
TY - UNPB
TI - Szarek and Ball made simple
AU - Colin Tang
AU - Tomasz Tkocz
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28384
UR - https://arxiv.org/abs/2610.28384
AB - We present proofs of Szarek's moment comparison and Ball's cube slicing inequalities based on elementary convexity and majorisation. The key ingredient is a moment-lifting argument which allows us to use Schur monotonicity, avoiding the integral inequalities used in the original Fourier-analytic approaches.
ER -