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Higher-order convex orders under free multiplicative convolution

Year: 2026

Type: preprint

Abstract: We prove that free multiplicative convolution with a probability measure on $[0,\infty)$ preserves the $k$-convex order for every integer $k\ge2$, 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 $\mathbb{R}$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29258

Author: Soong, Cheng-Xuan

Institutions: National Taiwan University, National Center for Theoretical Sciences, Mathematics Division

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223248171

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