Liu, JG; Zhang, Y, *Convergence of diffusion-drift many particle systems in probability under a sobolev norm*, Proceedings of Particle Systems and Partial Differential Equations - III,
Springer Proceedings in Mathematics and Statistics, vol. 162
(January, 2016),
pp. 195-223, Springer [doi] .
**Abstract:**

*© Springer International Publishing Switzerland 2016. In this paperwedevelop a newmartingale method to showthe convergence of the regularized empirical measure of many particle systems in probability under a Sobolev norm to the corresponding mean field PDE. Our method works well for the simple case of Fokker Planck equation and we can estimate a lower bound of the rate of convergence. This method can be generalized to more complicated systems with interactions.*