Dynamics of a tagged particle in the exclusion process

In this work we studied the Exclusion Process, one of the classical and most simple interacting particle systems, which has become a stochastic model for transport phenomena, such as cars in a traffic jam or dynamics of molecules in a gas. In particular, we have considered the Exclusion Process as Seen from a Tagged Particle, where one fixes the position of a distinguished particle at the origin, in order to analyze the evolution of the remaining particles, called "the environment", from the origin. For the Tagged Particle Process we stated and proved the main results in probability theory: the Law of Large Numbers, the Central Limit Theorem and an Invariane Principle, that holds in the Rough Path topology.