Kac's Process with Hard Potentials and a Moderate Angular Singularity

We investigate Kac's many-particle stochastic model of gas dynamics in the case of hard potentials with a moderate angular singularity, and show that the noncutoff particle system can be obtained as the limit of cutoff systems, with a rate independent of the number of particles \(N\). As consequences, we obtain a wellposedness result for the corresponding Boltzmann equation, and convergence of the particle system in the limit \(N\rightarrow \infty\).