TY - JOUR
T1 - Free transportation cost inequalities for noncommutative multi-variables
AU - Hiai, Fumio
AU - Ueda, Yoshimichi
N1 - Funding Information:
F.H. and Y.U. were supported in part by Japan Society for the Promotion of Science, Japan–Hungary Joint Project. F.H. was supported in part by Grant-in-Aid for Scientific Research (C)14540198 and by Strategic Information and Communications R&D Promotion Scheme of MPHPT and Y.U. was supported in part by Grant-in-Aid for Young Scientists (B)14740118.
PY - 2006/9
Y1 - 2006/9
N2 - 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.
AB - 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.
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U2 - 10.1142/S0219025706002457
DO - 10.1142/S0219025706002457
M3 - Article
AN - SCOPUS:33748521849
VL - 9
SP - 391
EP - 412
JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics
JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics
SN - 0219-0257
IS - 3
ER -