Before revision: We prove a rate of convergence of order 1/N for the N-particle approximation of a second-order partial differential equation in the space of probability measures, like the Master equation or Bellman equation of mean-field control problem under common noise  for the L^2-error on its L-derivative \partial_\mu v} .
After revision: We prove a rate of convergence of order 1/N for the N-particle approximation of a second-order partial differential equation in the space of probability measures, like the Master equation or Bellman equation of mean-field control problem under common noise . The rate is of order 1/N for the pathwise error on the solution v and of order 1/\sqrt{N for the L^2-error on its L-derivative \partial_\mu v} .