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

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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 Lₙ at any fixed time prior to the critical time. The asymptotic behavior of Lₙ 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) Lₙ has logarithmic order of growth while higher speeds (``warm'' gas) yield polynomial rates for Lₙ.