Interacting particle systems with partial annihilation through membranes

Abstract

This thesis studies the <italic>hydrodynamic limit</italic> and the <italic>fluctuation limit</italic> for a class of interacting particle systems in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. However, they are general microscopic models that can describe a variety of macroscopic phenomena with coupled boundary conditions, such as the population dynamics of two segregated species under competition. Proving these two types of limits represents establishing the <italic>functional law of large numbers</italic> and the <italic>functional central limit theorem</italic>, respectively, for the time-trajectory of the particle densities. This also corresponds to the study of the behavior of the system at two different scales. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation.