On Convex Bodies and Log-Concave Probability Measures with Unconditional Basis

@inproceedings{Bobkov2003OnCB,
title={On Convex Bodies and Log-Concave Probability Measures with Unconditional Basis},
author={Sergey G. Bobkov and F. L. Nazarov},
year={2003}
}

We consider here two asymptotic properties of finite dimensional convex bodies which generate a norm with an unconditional basis. For definiteness, such a basis is taken to be the canonical basis in R. Thus, assume we are given a convex set K ⊂ R of volume voln(K) = 1 which, together with every point x = (x1, . . . , xn), contains the parallepiped with the sides [−|xj |, |xj | ], 1 ≤ j ≤ n. In addition, K is supposed to be in isotropic position, which is equivalent to the property that the… CONTINUE READING