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

Philippe Biane·Dan Voiculescu
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Abstract

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.

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Philippe Biane, Dan Voiculescu. 2000-06-06. A Free Probability Analogue of the Wasserstein Metric on the Trace-State Space. https://arxiv.org/abs/math/0006044

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