Random Euclidean sections of some classical Banach spaces - Gordon, Y.; Guédon, O.; Meyer, M.; Pajor, A. (Mathematica Scandinavica, 2002)
Using probabilistic arguments, we give precise estimates of the Banach-Mazur distance of subspaces of the classical _q^n spaces and of Schatten classes of operators S_q^n for q 2 to the Euclidean space. We also estimate volume ratios of random subspaces of a normed space with respect to subspaces of quotients of _q. Finally, the preceeding methods are applied to give estimates of Gelfand numbers of some linear operators.