Stochastic domination for iterated convolutions and catalytic majorization

Guillaume Aubrun (1) , Ion Nechita (1)

1 ICJ - Institut Camille Jordan

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.

Mots clés: stochastic ordering; majorization; catalytic majorization

Domaines: Physique Quantique [quant-ph]; Probabilités [math.PR]

Guillaume Aubrun, Ion Nechita. Stochastic domination for iterated convolutions and catalytic majorization. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2009, 45 (3), pp.611-625. ⟨hal-00159197v2⟩