  We 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.
