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

Abstract

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.

Published at http://dx.doi.org/10.1214/009117904000000900 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)