The is somehow a sequel to the previous paper. 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 which are more precise that in the previous paper.

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aubrun (arrobas) math. univ-lyon1. fr