Diffusion Processes and the Ewens Sampling Formula

Crane [Statist. Sci. 31 (2016) 1–19] provides an excellent review of Ewens’ sampling formula (henceforth, ESF), its applications in and connections with various subjects. This note intends to extend the discussion a little bit. The focus will be on nonequilibrium ESF involving diffusion processes, ESF with symmetric selection and asymptotics of ESF. The references listed are by no means exhaustive.