Colloquium Mathematics R. Szabó

Title

Inhomogeneous contact process and percolation

Abstract:

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.