We consider a family of distributions on spatial random partitions that provide a coupling between different models of interest: the ideal Bose gas; the zero-range process; particle clustering; and spatial permutations. These distributions are invariant for a "chain of Chinese restaurants" stochastic process. We obtain results for the distribution of the size of the largest component.
"Random partitions in statistical mechanics." Electron. J. Probab. 19 1 - 37, 2014. https://doi.org/10.1214/EJP.v19-3244