The equilibrium states and the time asymptotic behavior of Spitzer's zero-range interaction scheme are studied in the case of a positive-recurrent, irreducible single particle law and an attractive speed function. It is shown that within the natural phase space of finitely many particles per cell, clusters occur which lead time-asymptotically to infinite occupancy by certain individual cells. These cells are then identified in terms of the parameters of the model.
Ed Waymire. "Zero-Range Interaction at Bose-Einstein Speeds Under a Positive Recurrent Single Particle Law." Ann. Probab. 8 (3) 441 - 450, June, 1980. https://doi.org/10.1214/aop/1176994719