Motion by curvature and large deviations for an interface dynamics on ℤ2

We study large deviations for a Markov process on curves in Z 2 mimicking the motion of an interface.Our dynamics can be tuned with a parameter β, which plays the role of an inverse temperature and coincides at β = ∞ with the zero temperature Ising model Glauber dynamics, where curves correspond to the boundaries of droplets of one phase immersed in a sea of the other one.The diffusion coefficient and mobility of the model are identified and correspond to those predicted in the literature.We prove that contours typically follow a motion by curvature with an influence of the parameter β and establish large deviation bounds at all large enough β < ∞.