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Free transportation cost inequalities via random matrix approximation
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  • Published: 29 April 2004

Free transportation cost inequalities via random matrix approximation

  • Fumio Hiai1,
  • Dénes Petz2 &
  • Yoshimichi Ueda3 

Probability Theory and Related Fields volume 130, pages 199–221 (2004)Cite this article

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  • 22 Citations

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Abstract.

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.

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Author information

Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, 980-8579, Japan

    Fumio Hiai

  2. Department for Mathematical Analysis, Budapest University of Technology and Economics, H-1521, Budapest XI., Hungary

    Dénes Petz

  3. Graduate School of Mathematics, Kyushu University, Fukuoka, 810-8560, Japan

    Yoshimichi Ueda

Authors
  1. Fumio Hiai
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  2. Dénes Petz
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  3. Yoshimichi Ueda
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Additional information

Supported in part by Grant-in-Aid for Scientific Research (C)14540198 and by the program “R&D support scheme for funding selected IT proposals” of the Ministry of Public Management, Home Affairs, Posts and Telecommunications.

Supported in part by MTA-JSPS project (Quantum Probability and Information Theory) and by OTKA T032662.

Supported in part by Grant-in-Aid for Young Scientists (B)14740118.

Mathematics Subject Classification (2000): Primary: 46L54, 46L53; Secondary: 60F10, 15A52, 94A17.

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Hiai, F., Petz, D. & Ueda, Y. Free transportation cost inequalities via random matrix approximation. Probab. Theory Relat. Fields 130, 199–221 (2004). https://doi.org/10.1007/s00440-004-0351-1

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  • Received: 06 November 2003

  • Revised: 29 January 2004

  • Published: 29 April 2004

  • Issue Date: October 2004

  • DOI: https://doi.org/10.1007/s00440-004-0351-1

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Key words and phrases:

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