Free transportation cost inequalities for noncommutative multi-variables

Fumio Hiai, Yoshimichi Ueda

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 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
Volume9
Issue number3
DOIs
Publication statusPublished - Sep 1 2006

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Free Entropy
Wasserstein Distance
costs
Matrix Approximation
convexity
Relative Entropy
Probability Space
Costs
Random Matrices
Square root
Convexity
Entropy
entropy
analogs
Analogue
approximation
Framework

All Science Journal Classification (ASJC) codes

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

Cite this

Free transportation cost inequalities for noncommutative multi-variables. / Hiai, Fumio; Ueda, Yoshimichi.

In: Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 9, No. 3, 01.09.2006, p. 391-412.

Research output: Contribution to journalArticle

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