Stochastic domination for iterated convolutions and catalytic majorization

Guillaume Aubrun; Ion Nechita

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 3, page 611-625
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Aubrun, Guillaume, and Nechita, Ion. "Stochastic domination for iterated convolutions and catalytic majorization." Annales de l'I.H.P. Probabilités et statistiques 45.3 (2009): 611-625. <http://eudml.org/doc/78036>.

@article{Aubrun2009,
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.},
author = {Aubrun, Guillaume, Nechita, Ion},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stochastic domination; iterated convolutions; large deviations; majorization; catalysis},
language = {eng},
number = {3},
pages = {611-625},
publisher = {Gauthier-Villars},
title = {Stochastic domination for iterated convolutions and catalytic majorization},
url = {http://eudml.org/doc/78036},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Aubrun, Guillaume
AU - Nechita, Ion
TI - Stochastic domination for iterated convolutions and catalytic majorization
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 3
SP - 611
EP - 625
AB - 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.
LA - eng
KW - stochastic domination; iterated convolutions; large deviations; majorization; catalysis
UR - http://eudml.org/doc/78036
ER -

References

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