Talagrand Inequality for the Semicircular Law and Energy of the Eigenvalues of Beta Ensembles
نویسنده
چکیده
Abstract We give a short proof of the free analogue of the Talagrand inequality for the transportation cost to the semicircular which was originally proved in [1]. The proof is based on a convexity argument and is in the spirit of the original Talagrand’s proof from [8]. We also discuss the convergence, fluctuations and large deviations of the energy of the eigenvalues of β ensembles, which gives also yet another proof of the convergence of the eigenvalue distribution to the semicircle law.
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تاریخ انتشار 2006