Threshold for the expected measure of the convex hull of random points with independent coordinates

Abstract

AbstractLet be an even Borel probability measure on . For every , consider independent random vectors in , with independent coordinates having distribution . We establish a sharp threshold for the product measure of the random polytope in under the assumption that the Legendre transform of the logarithmic moment generating function of satisfies the condition where . An application is a sharp threshold for the case of the product measure , with density , where is the ‐norm and .