Free transportation cost inequalities for noncommutative multi-variables

Fumio Hiai, Yoshimichi Ueda

Research output: Contribution to journalArticlepeer-review

6 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 - Sep 2006

All Science Journal Classification (ASJC) codes

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


Dive into the research topics of 'Free transportation cost inequalities for noncommutative multi-variables'. Together they form a unique fingerprint.

Cite this