Energy and number of clusters in stochastic systems of sticky gravitating particles

We consider a one-dimensional model of a gravitational gas. The gas consists of $n$ particles whose initial positions and speeds are random. At collisions particles stick together, forming “clusters.” Our main goal is to study the properties of the gas as $n\to\infty$. We separately consider “cold gas” (each particle has zero initial speed) and “warm gas” (each particle has nonzero initial speed). For the cold gas, the asymptotics of the number of clusters $K_n(t)$ is studied. We also explore the kinetic energy $E_n(t)$. It is proved that the warm gas instantly “cools,” i.e., $E_n(+0)\to 0$ as $n\to\infty$.