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arXiv · 2403.15682

Measure comparison problems for dilations of convex bodies

Malak Lafi·Artem Zvavitch
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Abstract

We study a version of the Busemann-Petty problem for $\log$-concave measures with an additional assumption on the dilates of convex, symmetric bodies. One of our main tools is an analog of the classical large deviation principle applied to $\log$-concave measures, depending on the norm of a convex body. We hope this will be of independent interest.

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Malak Lafi, Artem Zvavitch. 2024-03-23. Measure comparison problems for dilations of convex bodies. https://doi.org/10.4153/s0008439524000729

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