We show that some classical asymptotic results valid for covariance matrices of vectors with independent coefficients (such as the Marcenko-Pastur and the Bai-Yin theorems) are also valid for vectors uniformly distributed on the unit ball of the finite dimensional l_p spaces.
The Marcenko-Pastur theorem has been extended to general convex bodies by Pajor and Pastur.
aubrun (arrobas) math. univ-lyon1. fr