Geodesic
Aggregation rates in one-dimensional stochastic gas model with finite polynomial moments of particle speeds
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 158-179

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We consider one-dimensional system of auto-gravitating sticky particles with random initial speeds and describe the process of aggregation in terms of the largest cluster size $L_n$ at any fixed time prior to the critical time. We study the asymptotic behavior of $L_n$ for the warm gas, i.e., for a system of particles with nonzero initial speeds $v_i(0)=u_i$, where $(u_i)$ is a family of i.i.d. random variables with mean zero, unit variance and finite $p$-th moment $E(|u_i|^p)\infty$, $p\ge 2$, and obtain sharp lower and upper bounds for $L_n(t)$. 
@article{ZNSL_2007_351_a8,
     author = {V. F. Zakharova},
     title = {Aggregation rates in one-dimensional stochastic gas model with finite polynomial moments of particle speeds},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {158--179},
     publisher = {mathdoc},
     volume = {351},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a8/}
}
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V. F. Zakharova. Aggregation rates in one-dimensional stochastic gas model with finite polynomial moments of particle speeds. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 158-179. http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a8/