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 μ*n is stochastically dominated by ν*n for two given probability measures μ and ν. As a consequence we obtain a similar theorem on the majorization order for vectors in Rd. In particular we prove results about catalysis in quantum information theory.
Publié le : 2009-08-15
Classification:
Stochastic domination,
Iterated convolutions,
Large deviations,
Majorization,
Catalysis,
60E15,
94A05
@article{1249391377,
author = {Aubrun, Guillaume and Nechita, Ion},
title = {Stochastic domination for iterated convolutions and catalytic majorization},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 611-625},
language = {en},
url = {http://dml.mathdoc.fr/item/1249391377}
}
Aubrun, Guillaume; Nechita, Ion. Stochastic domination for iterated convolutions and catalytic majorization. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 611-625. http://gdmltest.u-ga.fr/item/1249391377/