Free transportation cost inequalities for noncommutative multi-variables

Fumio Hiai, Yoshimichi Ueda

研究成果: ジャーナルへの寄稿学術誌査読

6 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)391-412
ページ数22
ジャーナルInfinite Dimensional Analysis, Quantum Probability and Related Topics
9
3
DOI
出版ステータス出版済み - 9月 2006

!!!All Science Journal Classification (ASJC) codes

  • 統計物理学および非線形物理学
  • 統計学および確率
  • 数理物理学
  • 応用数学

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