The parabolic Anderson model (PAM), which is the Cauchy problem for the heat equation with random potential. The PAM is a mathematical model that describes how mass (i.e. matter or energy) flows in... Show moreThe parabolic Anderson model (PAM), which is the Cauchy problem for the heat equation with random potential. The PAM is a mathematical model that describes how mass (i.e. matter or energy) flows in a medium in the presence of a field of sources and sinks.The PAM has been extensively studied on regular lattices and is well understood there. However, the lattice is not always a suitable model and we look for extensions to random graphs. Very little is known for general graphs and the literature is extremely sparse. The present thesis is a contribution to this developing area. Because sparse random graphs can often be approximated by trees, the natural first step is to consider the PAM on a tree. In particular, this thesis is devoted to studying the PAM on random trees. Show less
