Inequalities related to free entropy derived from random matrix approximation

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dc.creatorHiai, Fumio
dc.creatorPetz, Denes
dc.creatorUeda, Yoshimichi
dc.date2003-10-29
dc.date.accessioned2026-07-07T05:02:19Z
dc.date.available2026-07-07T05:02:19Z
dc.descriptionBiane proved the free analog of the logarithmic Sobolev inequality for probability measures on the real line by means of random matrix approximation procedure. We show that the same method can be applied to reprove Biane and Voiculescu's free analog of Talagrand's transportation cost inequality for measures on the real line. Furthermore, we prove the free analogs of the logarithmic Sobolev inequality and the transportation cost inequality for measures on 1-dimensional torus as well by extending the method to special unitary random matrices.
dc.identifierhttps://arxiv.org/abs/math/0310453
dc.identifierhttp://arxiv.org/abs/math/0310453
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69011
dc.subjectOperator Algebras
dc.subjectProbability
dc.titleInequalities related to free entropy derived from random matrix approximation
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