A free probability analogue of the Wasserstein metric on the trace-state space |
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| Authors: | P. Biane D. Voiculescu |
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| Affiliation: | (1) CNRS, DMA, école Normale Supérieure, 45 Rue d'Ulm, 75005 Paris, France, e-mail: biane@dmi.ens.fr, FR;(2) Department of Mathematics, University of California, Berkeley, California 94720—3840, USA, e-mail: dvv@math.berkeley.edu, US |
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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. Submitted: August 2000. |
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