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Higher-order convex orders under free additive convolution
Abstract
We prove that free additive convolution preserves the k-convex order for every k≥2, 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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BibTeX
@misc{soong2026higherorder,
title = {{Higher-order convex orders under free additive convolution}},
author = {Cheng-Xuan Soong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35901},
eprint = {2609.35901},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35901},
}
RIS
TY - UNPB
TI - Higher-order convex orders under free additive convolution
AU - Cheng-Xuan Soong
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35901
UR - https://arxiv.org/abs/2609.35901
AB - We prove that free additive convolution preserves the k-convex order for every k≥2, 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.
ER -