The Symmetric Exclusion Process and the Gausian Free Field on compact Riemannian manifolds

In this thesis we study the Symmetric Exclusion Process (SEP) and the Discrete Gaussian Free Field (DGFF) on compact Riemannian manifolds. In particular, we obtain the hydrodynamic limit and the equilibrium fluctuations of SEP and we show that the DGFF converges to its continuous counterpart. To define these discrete models, we construct grids...