Best possible sufficient conditions for strong law of large numbers for multi-indexed orthogonal random elements.
Between Paouris concentration inequality and variance conjecture
We prove an almost isometric reverse Hölder inequality for the euclidean norm on an isotropic generalized Orlicz ball which interpolates Paouris concentration inequality and variance conjecture. We study in this direction the case of isotropic convex bodies with an unconditional basis and the case of general convex bodies.