A Deterministic Proof of the Slicing Theorem

Silouanos Brazitikos

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arXiv · 2608.14342

A Deterministic Proof of the Slicing Theorem

Silouanos Brazitikos

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Abstract

We give a deterministic proof of Bourgain's slicing theorem. The proof uses neither stochastic localization nor stochastic calculus, does not rely on Guan's covariance bound, and avoids $M$-ellipsoids, Pisier's regularization machinery, and complex interpolation. Instead, the argument is based on a deterministic one-parameter quadratic perturbation of the measure, a covariance-survival principle, and a geometric analysis of $L_p$-centroid bodies.

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Silouanos Brazitikos. 2026-08-14. A Deterministic Proof of the Slicing Theorem. https://arxiv.org/abs/2608.14342

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