On Ƶp-Norms of Random Vectors

Аннотация

To any n-dimensional random vector X we may associate its L_p-centroid body Ƶ_p (X) and the corresponding norm. We formulate a conjecture concerning the bound on the Ƶ_p (X)-norm of X and show that it holds under some additional symmetry assumptions. We also relate our conjecture to estimates of covering numbers and Sudakov-type minoration bounds.