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

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

2003-11-03

arxiv.org/abs/cond-mat/0311025v2

Annals of Probability 2005, Vol. 33, No. 1, 53-81

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1214/009117904000000900

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.

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