Self-diffusion constants of non-colliding interacting Brownian motions in one spatial dimension

Abstract

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.

arXiv comment20 pages, published in RIMS K\hat{o}ky\hat{u}roku Bessatsu B59. Typos are corrected. The list of the corrections of typos is given in the last page