Free transportation cost inequalities for noncommutative multi-variables

Fumio Hiai, Yoshimichi Ueda

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)


    The free analogue of the transportation cost inequality so far obtained for measures is extended to the noncommutative setting. Our free transportation cost inequality is for traded distributions of noncommutative self-adjoint (also unitary) multi-variables in the framework of tracial C*-probability spaces, and it tells that the Wasserstein distance is dominated by the square root of the relative free entropy with respect to a potential of additive type (corresponding to the free case) with some convexity condition. The proof is based on random matrix approximation procedure.

    Original languageEnglish
    Pages (from-to)391-412
    Number of pages22
    JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
    Issue number3
    Publication statusPublished - Sept 2006

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Mathematical Physics
    • Applied Mathematics


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