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math.OA2000★ 1 cited
A Free Probability Analogue of the Wasserstein Metric on the Trace-State Space
Philippe Biane, Dan Voiculescu
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…
math.RA2000★ 18 cited
A Note on Cyclic Gradients
Dan Voiculescu
Simple necessary and sufficient conditions for a -tuple of noncommutative polynomials to be a cyclic gradient are given and similarly for a noncommutative polynomial to have a v…