A Free Probability Analogue of the Wasserstein Metric on the Trace-State Space

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We define a free probability analogue of the Wasserstein metric, which extends the classical one. In dimension one, we prove that the square of the Wasserstein distance to the semi-circle distribution is majorized by a modified free entropy quantity.
14 pages, Incomplete Preliminary Version

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Operator Algebras, 46L54; 60E99; 94A17

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http://salesiana.dossiersoluciones.com/handle/123456789/59360

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0006044
 http://arxiv.org/abs/math/0006044

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arXiv