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arXiv · 2609.35901

Higher-order convex orders under free additive convolution

Cheng-Xuan Soong
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Abstract

We prove that free additive convolution preserves the $k$-convex order for every $k\ge2$, assuming finite $(k-1)$st absolute moments for the compared measures and a finite $\max\{2,k-1\}$th absolute moment for the convolving measure. In particular, the case $k=4$ gives an affirmative answer to a question of Heinävaara concerning fourth-order convolution comparison.

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Cheng-Xuan Soong. 2026-09-28. Higher-order convex orders under free additive convolution. https://arxiv.org/abs/2609.35901

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