  We study measures on random partitions, arising from condensing stochastic
particle systems with stationary product distributions. We provide fairly
general conditions on the stationary weights, which lead to Poisson-Dirichlet
statistics of the condensed phase in the thermodynamic limit. The
Poisson-Dirichlet distribution is known to be the unique reversible measure of
split-merge dynamics for random partitions, which we use to characterize the
limit law. We also establish concentration results for the macroscopic phase,
using size-biased sampling techniques and the equivalence of ensembles to
characterize the bulk distribution of the system.
