We introduce and study interval partition diffusions with Poisson–Dirichlet stationary distribution for parameters and . This extends previous work on the cases and and builds on our recent work on measure-valued diffusions. Our methods for dealing with general allow us to strengthen previous work on the special cases to include initial interval partitions with dust. In contrast to the measure-valued setting, we can show that this extended process is a Feller process improving on the Hunt property established in that setting. These processes can be viewed as diffusions on the boundary of a branching graph of integer compositions. Indeed, by studying their infinitesimal generator on suitable quasi-symmetric functions, we relate them to diffusions obtained as scaling limits of composition-valued up-down chains.
Electron. J. Probab.
28:
1-46
(2023).
DOI: 10.1214/23-EJP946