In a previous paper, we showed that gradient maps of exponentially concave functions provide solutions to a Monge–Kantorovich optimal transport problem and give a better gradient approximation than ...

Convex geometry is a vibrant area of mathematics that investigates the properties and structure of convex sets in Euclidean spaces. This field is intrinsically linked to a series of fundamental ...

In this paper we build the increasing convex (concave) order for the scalar product of random vectors with an upper (lower) tail permutation decreasing joint density. As applications, we revisit ...