  In this paper, we derive rigorously a non-local cross-diffusion system from
an interacting stochastic many-particle system in the whole space. The
convergence is proved in the sense of probability by introducing an
intermediate particle system with a mollified interaction potential, where the
mollification is of algebraic scaling. The main idea of the proof is to study
the time evolution of a stopped process and obtain a Gronwall type estimate by
using Taylor's expansion around the limiting stochastic process.
