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A free probability analogue of the Wasserstein metric on the trace-state space

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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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Authors and Affiliations

  1. CNRS, DMA, École Normale Supérieure, 45 Rue d'Ulm, 75005 Paris, France, e-mail: biane@dmi.ens.fr, , , , , , FR

    P. Biane

  2. Department of Mathematics, University of California, Berkeley, California 94720—3840, USA, e-mail: dvv@math.berkeley.edu, , , , , , US

    D. Voiculescu

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  1. P. Biane
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  2. D. Voiculescu
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Submitted: August 2000.

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Biane, P., Voiculescu, D. A free probability analogue of the Wasserstein metric on the trace-state space. GAFA, Geom. funct. anal. 11, 1125–1138 (2001). https://doi.org/10.1007/s00039-001-8226-4

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  • DOI: https://doi.org/10.1007/s00039-001-8226-4

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