Concentration of mass on convex bodies
Abstract
We establish sharp concentration of mass inequality for isotropic convex bodies: there exists an absolute constant c > 0 such that if K is an isotropic convex body in R-n, then Prob ({x is an element of K : parallel to x parallel to(2) >= c root nL(K)t}) <= exp (-root nt) for every t >= 1, where L-K denotes the isotropic constant.