Aggregation in one-dimensional gas model with stable initial data

One-dimensional stochastic model of gravitationally interacting adhesive particles with distribution of initial velocities from the domain of normal attraction of stable law is considered. It is shown that a nonrandom critical time exists when initial velocities are small enough. Namely, no macroscopic clusters appear before the critical time, while after the critical time almost all mass is concentrated in a single cluster. The order of maximal cluster size for times prior to critical is obtained. If velocities are large enough, then macroscopic clusters appear right after the beginning of system's life, but complete aggregation does not occur within finite time.