  We investigate the diffusion of a grain boundary in a crystalline material.
We consider in particular the case of a regularly spaced low-angle grain
boundary schematized as an array of dislocations that interact with each other
through long-range stress fields and with the crystalline Peierls-Nabarro
potential. The methodology employed to analyze the dynamics of the center of
mass of the grain boundary and its spatio-temporal fluctuations is based on
over-damped Langevin equations. The generality and the efficiency of this
technique is proved by the agreement with molecular dynamics simulations.
