Talagrand Inequality for the Semicircular Law and Energy of the Eigenvalues of Beta Ensembles

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dc.creatorPopescu, Ionel
dc.date2006-10-27
dc.date2008-02-18
dc.date.accessioned2026-07-07T09:21:18Z
dc.date.available2026-07-07T09:21:18Z
dc.descriptionWe give a short proof of the free analogue of the Talagrand inequality for the transportation cost to the semicircular which was originally proved by Biane and Voiculescu. The proof is based on a convexity argument and is in the spirit of the original Talagrand's proof. We also discuss the convergence, fluctuations and large deviations of the energy of the eigenvalues of beta ensembles, which gives also yet another proof of the convergence of the eigenvalue distribution to the semicircle law.
dc.descriptionThis is the final version. There were some typos and minor errors fixed
dc.identifierhttps://arxiv.org/abs/math/0610826
dc.identifierhttp://arxiv.org/abs/math/0610826
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154973
dc.subjectClassical Analysis and ODEs
dc.subjectProbability
dc.subject46L54;15A52;60F10
dc.titleTalagrand Inequality for the Semicircular Law and Energy of the Eigenvalues of Beta Ensembles
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