Coin Tossing, Random Mirrors and Dependent Percolation: Three Paradigms of PhaseTransition

摘要

In this thesis, we consider three models that undergo different types of phasetransitions. In the first chapter, we introduce the three models and give some background for them. The rest of the thesis consists of three papers studying these models, with separate chapters giving commentary and proving results mentioned. Our first model is related to random walks on coloring. Secondly, we consider a dependent bond percolation model. Finally, we consider a Lorentz Gas type model.