Probability Theory and Related Fields

, Volume 130, Issue 2, pp 199–221

Free transportation cost inequalities via random matrix approximation

  • Fumio  Hiai
  • Dénes  Petz
  • Yoshimichi Ueda


By means of random matrix approximation procedure, we re-prove Biane and Voiculescu’s free analog of Talagrand’s transportation cost inequality for measures on R in a more general setup. Furthermore, we prove the free transportation cost inequality for measures on T as well by extending the method to special unitary random matrices.

Key words and phrases:

Transportation cost inequality Free probability Random matrix Wasserstein distance Free entropy Relative free entropy 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Fumio  Hiai
    • 1
  • Dénes  Petz
    • 2
  • Yoshimichi Ueda
    • 3
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Department for Mathematical AnalysisBudapest University of Technology and EconomicsBudapest XI.Hungary
  3. 3.Graduate School of MathematicsKyushu UniversityFukuokaJapan

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