Hydrodynamical Limit and Large Deviations Principle for the Exclusion Process with Slow Bonds

Adriana Neumann

Keywords: Slow bond; Hydrodynamical limit; Large deviations

This PhD thesis consists of three parts, all of them related to the symmetric exclusion process in the presence of slow bonds, which are particular bonds with smaller rate of passage of particles, called conductance. The first part is a large deviation principle for the scaling limit of empirical measure, containing also the hydrodynamical limit of the symmetric exclusion process with slow bonds and the hydrodynamical limit of weakly asymmetric exclusion process with slows bonds. The second part deals with the hydrodynamical limit of the empirical measure in the presence of slow bonds with conductance $N^{-\beta}$, where $N$ is the scaling parameter. Three different behaviors are exhibited, corresponding to the cases $\beta\in [0,1)$, $\beta=1$ or $\beta>1$. The third part is a $d$-dimensional problem. There, the slow bonds have a spatial position associated to a smooth closed surface, modeling a membrane slowing down the passage of particles. It is presented the hydrodynamical limit of such model.

Anexos:

• tese_Adriana.pdf