On long time behavior of some coagulation processes

We consider an infinite system of particles characterized by their position and mass, in which coalescence occurs. Each particle endures Brownian excitation, and is subjected to the attraction of a potential. We define a stochastic process (Xt,Mt)t⩾0 describing the evolution of the position and mass of a typical particle. We show that under some conditions, the mass process Mt tends almost surely to infinity, while the position process Xt tends almost surely to 0, as time tends to infinity.