ON THE CARDINALITY OF COLLISIONAL CLUSTERS FOR HARD SPHERES AT LOW DENSITY

We resume the investigation, started in [2], of the statistics of backward clusters in a gas of N hard spheres of small diameter epsilon. A backward cluster is defined as the group of particles involved directly or indirectly in the backwards-in-time dynamics of a given tagged sphere. We obtain an estimate of the average cardinality of clusters with respect to the equilibrium measure, global in time, uniform in epsilon, N for epsilon(2) N = 1 (Boltzmann-Grad regime).

Automated summary

The study continues to investigate the statistics of backward clusters in a gas of N hard spheres of small diameter epsilon, providing an estimate of the average cardinality of clusters with respect to the equilibrium measure under specific conditions in the system of hard spheres.