Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Stochastic domination for iterated convolutions and catalytic majorization

Guillaume Aubrun and 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 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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist. Volume 45, Number 3 (2009), 611-625.

Dates
First available in Project Euclid: 4 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1249391377

Digital Object Identifier
doi:10.1214/08-AIHP175

Mathematical Reviews number (MathSciNet)
MR2548496

Zentralblatt MATH identifier
1179.60008

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 94A05: Communication theory [See also 60G35, 90B18]

Keywords
Stochastic domination Iterated convolutions Large deviations Majorization Catalysis

Citation

Aubrun, Guillaume; Nechita, Ion. Stochastic domination for iterated convolutions and catalytic majorization. Ann. Inst. H. Poincaré Probab. Statist. 45 (2009), no. 3, 611--625. doi:10.1214/08-AIHP175. https://projecteuclid.org/euclid.aihp/1249391377


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