Free transportation cost inequalities via random matrix approximation |
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| Authors: | Fumio Hiai Dénes Petz Yoshimichi Ueda |
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| Institution: | (1) Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, 980-8579, Japan;(2) Department for Mathematical Analysis, Budapest University of Technology and Economics, H-1521 Budapest XI., Hungary;(3) Graduate School of Mathematics, Kyushu University, Fukuoka, 810-8560, Japan |
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| Abstract: | By means of random matrix approximation procedure, we re-prove Biane and Voiculescu s free analog of Talagrands transportation cost inequality for measures on R in a more general setup. Furthermore, we prove the free transportation cost inequality for measures on T as well by extending the method to special unitary random matrices.Supported in part by Grant-in-Aid for Scientific Research (C)14540198 and by the program  R&D support scheme for funding selected IT proposals of the Ministry of Public Management, Home Affairs, Posts and Telecommunications.Supported in part by MTA-JSPS project (Quantum Probability and Information Theory) and by OTKA T032662.Supported in part by Grant-in-Aid for Young Scientists (B)14740118.Mathematics Subject Classification (2000): Primary: 46L54, 46L53; Secondary: 60F10, 15A52, 94A17. |
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| Keywords: | Transportation cost inequality Free probability Random matrix Wasserstein distance Free entropy Relative free entropy |
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