Self-diffusion constants of non-colliding interacting Brownian motions   in one spatial dimension
  We prove that self-diffusion constants of interacting Brownian particles in $ \mathbb{R}$ always vanish if the particles do not collide with each other. We represent self-diffusion constants by additive functionals of reversible Markov processes as obtained in O. 1998. 
Hirofumi Osada
math.PR