A functional central limit theorem for interacting particle systems on   transitive graphs
  A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered diffusion process. As an application, a central limit theorem for certain hitting times, interpreted as failure times of a coherent system in reliability, is derived. 
Paul Doukhan, Gabriel Lang, Sana Louhichi, Bernard Ycart