Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System (Communications in Mathematical Research, 2023)
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 timeevolution of a stopped process and obtain a Grönwall type estimate by usingTaylor’s expansion around the limiting stochastic process.
Keywords: Stochastic particle systems; cross-diffusion system; mean-field limit; population dynamics.