Quantitative propagation of chaos for the Boltzmann equation with moderately soft potentials

We study the Kac particle system associated with the spatially homogeneous Boltzmann equation with non-cutoff collision kernels in the moderately soft potential regime $-1<\gamma<0$.

We prove uniqueness in law for the particle system and, in particular, establish an explicit convergence rate from the empirical measure of the Kac particle system to the weak solution of the Boltzmann equation in Wasserstein-2 distance, assuming that the initial datum $f_0$ has finite Fisher information and polynomial moments.

To the best of our knowledge, this provides the first quantitative convergence rate for the Kac particle system in the soft potential setting.