Stochastic domination for iterated convolutions and catalytic majorization
Annales de l'I.H.P. Probabilités et statistiques, Volume 45 (2009) no. 3, p. 611-625

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.

Nous étudions comment les convolutions itérées des mesures de probabilités se comparent pour la domination stochastique. Nous donnons des conditions nécessaires et suffisantes pour l'existence d'un entier n tel que μ*n soit stochastiquement dominée par ν*n, étant données deux mesures de probabilités μ et ν. Nous obtenons en corollaire un théorème similaire pour des vecteurs de Rd et la relation de Schur-domination. Plus spécifiquement, nous démontrons des résultats sur la catalyse en théorie quantique de l'information.

DOI : https://doi.org/10.1214/08-AIHP175
Classification:  60E15,  94A05
Keywords: stochastic domination, iterated convolutions, large deviations, majorization, catalysis
@article{AIHPB_2009__45_3_611_0,
     author = {Aubrun, Guillaume and Nechita, Ion},
     title = {Stochastic domination for iterated convolutions and catalytic majorization},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {45},
     number = {3},
     year = {2009},
     pages = {611-625},
     doi = {10.1214/08-AIHP175},
     zbl = {1179.60008},
     mrnumber = {2548496},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2009__45_3_611_0}
}
Aubrun, Guillaume; Nechita, Ion. Stochastic domination for iterated convolutions and catalytic majorization. Annales de l'I.H.P. Probabilités et statistiques, Volume 45 (2009) no. 3, pp. 611-625. doi : 10.1214/08-AIHP175. http://www.numdam.org/item/AIHPB_2009__45_3_611_0/

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