Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation

We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size L_n at any fixed time prior to the critical time. The asymptotic behavior of L_n is also analyzed for sequences of times tending to the critical time. A phenomenon of phase transition shows up, namely, for small initial particle speeds (cold'' gas) L_n has logarithmic order of growth while higher speeds (warm’’ gas) yield polynomial rates for L_n.