Propagation of Chaos for Moderately Interacting Particle Systems Related to Singular Kinetic McKean–Vlasov SDEs

Abstract. We study the propagation of chaos in a class of moderately interacting particle systems for the approximation of singular kinetic McKean–Vlasov SDEs driven by [Formula: see text]-stable processes. Diffusion parts include Brownian ([Formula: see text]) and pure-jump ([Formula: see text] perturbations, and interaction kernels are considered in a nonsmooth anisotropic Besov space. Using the Duhamel formula, sharp density estimates (recently issued in Hao, Röckner, and Zhang [ Ann. Probab ., 54 (2026), pp. 1–62]), and suitable martingale functional inequalities, we obtain direct estimates on the convergence rate between the empirical measure of the particle systems toward the McKean–Vlasov distribution. These estimates further lead to quantitative propagation of chaos results in the weak and strong sense.