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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 que
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