[Author]
 Vladislav Vysotsky

[Title]
 On energy and number of clusters in stochastic systems of sticky
 gravitating particles

[AMS Subj-class]
 82C22 Interacting particle systems
 60F05 Central limit and other weak theorems

[Abstract]
 We consider one-dimensional model of gravitational gas whose particles
 initially have random coordinates and speeds. While colliding, particles
 stick together forming "clusters". In the case of zero initial speeds
 ("cold gas") it has been studied the asymptotic behavior of number of
 clusters $K_n(t)$ as $n \to \infty$, where $n$ denotes the number of
 initial particles. We also explore the kinetic energy of gas $E_n(t)$.
 In the case of non-zero initial speeds ("warm gas") it's proved that
 the gas instantly "cools", i. e. $E_n(+0) \to 0$ as $n \to \infty$.
 The results are formulated in terms of convergence by probability. 

[Keywords]
 gravitational gas, sticky particles, non-elastic collisions,
 system of particles, number of clusters, energy

[Comments]
 LaTeX, English & Russian, 20 pp.
 The paper is accepted to "Theory of Probability and Its Applications".
 The paper contains 5 PostScript pictures (each in a separate file).

[Contact e-mail]
 vysotsky@vv9034.spb.edu