The parabolic Anderson model on Galton-Watson trees

Wang, D. (2024)

Doctoral Thesis

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.
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.

• Galton-Watson tree
• Parabolic Anderson model
• Random graphs
• Random walk in random environment
• Large deviations
• Feynman-Kac

• All authors: Wang, D.
• Supervisor: Hollander, W.T.F. den
• Committee: Derks, G.L.A.; Mandjes, M.R.H.; Köning, W.; Soares dos Santos, R.; Sousi, P.
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute (MI), Faculty of Science, Leiden University
• Date: 2024-05-28