Zero-Range Interaction at Bose-Einstein Speeds Under a Positive Recurrent Single Particle Law

Abstract

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.