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arXiv · 2510.00842

Monotonicity of the Gaussian measure under Banaszczyk transforms

Maud Szusterman
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Abstract

In the proof of his famous 5K-theorem, W. Banaszczyk introduced a transformation of convex bodies for which the Gaussian measure is monotone. In this note, we present a simplified proof of this monotonicity by slightly modifying Banaszczyk's transform, so that it interacts smoothly with Ehrhard symmetrizations, thereby yielding a somewhat easier proof of the 5K-theorem.

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Maud Szusterman. 2025-10-01. Monotonicity of the Gaussian measure under Banaszczyk transforms. https://arxiv.org/abs/2510.00842

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