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

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

2000-06-06

arxiv.org/abs/math/0006044v1

Mathematics

Operator Algebras

14 pages, Incomplete Preliminary Version

Scientific paper

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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