Cluster formation by inelastically colliding particles in one-dimensional space

Inelastically colliding particles moving in one-dimensional space are found to form clusters, each of which consists of particles with identical coordinates and velocities. There exists a critical size of a cluster, above which the cluster grows indefinitely by absorbing a colliding particle as if the collision were completely inelastic (rebound coefficient e = 0. It is experimentally found that when e = 0, the expected number of n-particle clusters is 1n, and the average number of final clusters 〈M〉 is 〈M〉 = ΣNn 11n, where N is the number of the particles in the system.