Dirichlet random walks

In this talk we will discuss some results obtained by Gerard Le Caer (J Stat Phys 2010, 2011) concerning Dirichlet random walks, namely convex combinations of points on a sphere with weights having Dirichlet distribution. The proofs are based on a kind of Stieltjes transform, suited for distributions on a ball, which has special properties with regard to the Dirichlet distribution. A limiting regime is considered, from which the means of Dirichlet processes come out.