FREE TRANSPORTATION COST INEQUALITIES FOR NONCOMMUTATIVE MULTI-VARIABLES

• HIAI, FUMIO

• UEDA, YOSHIMICHI

Abstract

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 tracial 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.

Journal

• Infinite Dimensional Analysis, Quantum Probability and Related Topics

  Infinite Dimensional Analysis, Quantum Probability and Related Topics 09 (03), 391-412, 2006

  World Scientific

Keywords

• Free probability theory
• random matrix
• operator algebras
• Wasserstein metric
• free entropy
• transportation cost inequality

Details

• CRID: 1050564288768521600
• NII Article ID: 120006714543
• HANDLE: 2237/00030626
• ISSN: 02190257
• Web Site: https://nagoya.repo.nii.ac.jp/records/28433
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • CiNii Articles