Contact processes on the integers

Achillefs Tzioufas

Published 2010-10-07, updated 2012-09-24Version 5

The three state contact process is the modification of the contact process at rate $\mu$ in which first infections occur at rate $\lambda$ instead. Chapters 2 and 3 consider the three state contact process on (graphs that have as set of sites) the integers with nearest neighbours interaction (that is, edges are placed among sites at Euclidean distance one apart). Results in Chapter 2 are meant to illustrate regularity of the growth of the process under the assumption that $\mu \geq \lambda$, that is, reverse immunization. While in Chapter 3 two results regarding the convergence rates of the process are given. Chapter 4 is concerned with the i.i.d.\ behaviour of the right endpoint of contact processes on the integers with symmetric, translation invariant interaction. Finally, Chapter 5 is concerned with two monotonicity properties of the three state contact process.