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arXiv · 2401.01033

On maximal intersection position for logarithmically concave functions and measures

Steven Hoehner·Michael Roysdon
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Abstract

A new position is introduced and studied for the convolution of log-concave functions, which may be regarded as a functional analogue of the maximum intersection position of convex bodies introduced and studied by Artstein-Avidan and Katzin (2018) and Artstein-Avidan and Putterman (2022). Our main result is a John-type theorem for the maximal intersection position of a pair of log-concave functions, including the corresponding decomposition of the identity. The main result holds under very weak assumptions on the functions; in particular, the functions considered may both have unbounded supports. As an application of our results, we introduce a John-type position for even $\log$-concave measures.

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Steven Hoehner, Michael Roysdon. 2024-01-02. On maximal intersection position for logarithmically concave functions and measures. https://arxiv.org/abs/2401.01033

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