Dissertation
The parabolic Anderson model on Galton-Watson trees
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 a medium in the presence of a field of sources and sinks.
- Author
- D. Wang
- Date
- 28 May 2024
- Links
- Thesis in Leiden Repository
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.