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arXiv · 0707.0211

Stochastic domination for iterated convolutions and catalytic majorization

Guillaume Aubrun·Ion Nechita
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Abstract

We study how iterated convolutions of probability measures compare under stochastic domination. We give necessary and sufficient conditions for the existence of an integer $n$ such that $\mu^{*n}$ is stochastically dominated by $\nu^{*n}$ for two given probability measures $\mu$ and $\nu$. As a consequence we obtain a similar theorem on the majorization order for vectors in $\R^d$. In particular we prove results about catalysis in quantum information theory.

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Guillaume Aubrun, Ion Nechita. 2007-07-02. Stochastic domination for iterated convolutions and catalytic majorization. https://doi.org/10.1214/08-aihp175

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