Exclusion with non reversible boundary dynamics

This thesis analyzes the behavior of the one and the two-point correlation function of two main models, first the Symmetric Simple Exclusion Process and second a non-linear version of it, both considered with slow boundaries, where the second model, for particular choices of the boundary rates, can resemble the first one. Using tools from Markov process theory, semigroup analysis, and stochastic calculus, we investigate estimates for the discrepancy between the full correlation function and the v-function. This requires an analysis of the behavior of the random walk that describes the evolution equation for the two-point correlation function. These estimates are crucial for justifying the derivation of hydrodynamic equations with correct boundary behavior and for understanding fluctuation structures in non-equilibrium systems.