Abstract

We study large deviations for a Markov process on curves in ${\mathbb{Z}}^2$ mimicking the motion of an interface. Our dynamics can be tuned with a parameter $\beta$, which plays the role of an inverse temperature and coincides at $\beta =\infty$ 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 $\beta$ and establish large deviation bounds at all large enough $\beta <\infty$.

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