arXiv subjects

Cheng-Xuan Soong

Publications and source records attributed to Cheng-Xuan Soong.

2 recordsLinked to original sources

arXiv2026

Higher-order convex orders under free multiplicative convolution

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 $\mathbb{R}$.

math.PR↗

arXiv2026

Higher-order convex orders under free additive convolution

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.

math.OA↗