Affiliation:
1. Department of Mathematics National and Kapodistrian University of Athens Athens Greece
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 .
Reference21 articles.
1. Encyclopedia of Mathematics and its Applications;Bingham N. H.,1989
2. Threshold phenomena for high-dimensional random polytopes
3. Phase transition for the volume of high‐dimensional random polytopes
4. S.Brazitikos A.Giannopoulos andM.Pafis Half‐space depth of log‐concave probability measures Preprint.
5. Threshold for the expected measure of random polytopes