Spectral flatness and the volume of intersections of p-ellipsoids

Motivated by classical works of Schechtman and Schmuckenschläger on intersections ℓp-balls recent ones in information-based complexity relating random sections ellipsoids the quality information approximation problems, we study threshold behavior asymptotic volume generalized p-ellipsoids. The non-critical is determined under a spectral flatness (Wiener entropy) condition semi-axes. In order to understand critical case at threshold, prove central limit theorem for q-norms points sampled uniformly from p-ellipsoid, which obtained Noether's