Random Points in Isotropic Convex Sets

Let K be a symmetric convex body of volume 1 whose inertia tensor is isotropic, i.e., for some constant L we have R K〈x, y〉2 dx = L2|y|2 for all y. It is shown that if m is about n(log n)3 then with high probability, this tensor can be approximately realised by an average over m independent random points chosen in K, 1 m m X