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Higher-order convex orders under free multiplicative convolution
Abstract
We prove that free multiplicative convolution with a probability measure on [0,∞) preserves the k-convex order for every integer k≥2, assuming finite (k−1)st absolute moments for the two measures being compared and for the convolving measure. The compared measures may have arbitrary support in ℝ.
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BibTeX
@misc{soong2026higherorder,
title = {{Higher-order convex orders under free multiplicative convolution}},
author = {Cheng-Xuan Soong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29258},
eprint = {2610.29258},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29258},
}
RIS
TY - UNPB
TI - Higher-order convex orders under free multiplicative convolution
AU - Cheng-Xuan Soong
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29258
UR - https://arxiv.org/abs/2610.29258
AB - We prove that free multiplicative convolution with a probability measure on [0,∞) preserves the k-convex order for every integer k≥2, assuming finite (k−1)st absolute moments for the two measures being compared and for the convolving measure. The compared measures may have arbitrary support in ℝ.
ER -