Distribution's template estimate with Wasserstein metrics
  In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an estimation of the mean distribution. Moreover, when the distributions are a common measure warped by a centered random operator, then the barycenter enables to recover this distribution template. 
Emmanuel Boissard (IMT), Thibaut Le Gouic (IMT), Jean-Michel Loubes   (IMT)
math.ST stat.TH