The well-posedness and regularity properties of diffusion-aggregation
equations, emerging from interacting particle systems, are established
on the whole space for bounded interaction force kernels by utilizing a
compactness convergence argument to treat the non-linearity as well as a
Moser iteration. Moreover, we prove a quantitative estimate in
probability with arbitrary algebraic rate between the approximative
interacting particle systems and the approximative McKean--Vlasov SDEs,
which implies propagation of chaos for the interacting particle systems.