FREE TRANSPORTATION COST INEQUALITIES FOR NONCOMMUTATIVE MULTI-VARIABLES

DOI10.1142/S0219025706002457zbMath1107.46045arXivmath/0501238OpenAlexW3105906109MaRDI QIDQ5493869

Fumio Hiai, Yoshimichi Ueda

Publication date: 16 October 2006

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0501238

zbMATH Keywords

free probability theoryWasserstein metricoperator algebrasrandom matrixfree entropytransportation cost inequality

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Free probability and free operator algebras (46L54) Random matrices (algebraic aspects) (15B52) Measures of information, entropy (94A17)

Related Items (5)

Tracial smooth functions of non-commuting variables and the free Wasserstein manifold ⋮ Notes on microstate free entropy of projections ⋮ Orbital free pressure and its Legendre transform ⋮ ORBITAL APPROACH TO MICROSTATE FREE ENTROPY ⋮ Duality for optimal couplings in free probability

Cites Work

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• Limit laws for random matrices and free products
• The analogues of entropy and of Fisher's information measure in free probability theory. II
• Large deviations for Wigner's law and Voiculescu's non-commutative entropy
• Free relative entropy for measures and a corresponding perturbation theory.
• A (one-dimensional) free Brunn-Minkowski inequality
• Transportation cost for Gaussian and other product measures
• Statistica mechanics of quantum spin systems. III
• Free analog of pressure and its Legendre transform
• FREE ENTROPY

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