A new proof of the Markov--Krein identity for distributions of means of Dirichlet processes

Natalia Tsilevich, Anatoly Vershik, and Marc Yor

We present a new simple proof of the Markov--Krein identity for distributions of means of Dirichlet processes. Our approach is based on a close relation of Dirichlet processes to gamma processes and basic properties of the gamma processes.