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arXiv · 2512.23179

An example of a non-log-concave distribution where the difference has a log-concave density

Min Wang
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Abstract

By the Pr\'ekopa-Leindler inequality, the difference $X-X'$ has a log-concave density provided that $X$ has a log-concave density and $X, X'$ are independent and identically distributed. We prove that the opposite direction does not always hold true by giving an explicit example.

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Min Wang. 2025-12-29. An example of a non-log-concave distribution where the difference has a log-concave density. https://doi.org/10.1137/s0040585x97t992069

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