Inhomogeneous contact process and percolation

In this thesis we study of the contact process - a particular type of interacting particle system - and different percolation models. Both the contact process and percolation are models of propagation of some material in an environment and have been the topic of intensive and fruitful research in the last decades due to their simplicity, rich behavior and mathematical tractability. Moreover, results often transfer from one model to the other, as a specific type of oriented percolation model can be viewed as a discrete-time version of the contact process.
We have studied how the introduction of inhomogeneities in the environment affects the behavior of the models. In general, random processes on infinite volume do not depend too much on local changes in the environment. In percolation models we can study how changing a small portion of the environment affects the occurrence of percolation. In the case of the contact process, since a single site or edge can affect the dynamics infinitely many times, one can ask whether its presence has an influence on the critical parameter of the process.