Random growth on a Ramanujan graph
arXiv:1908.09575
Abstract
The behavior of a certain random growth process is analyzed on arbitrary regular and non-regular graphs. Our argument is based on the Expander Mixing Lemma, which entails that the results are strongest for Ramanujan graphs, which asymptotically maximize the spectral gap. Further, we consider Erdős--Rényi random graphs and compare our theoretical results with computational experiments on flip graphs of point configurations. The latter is relevant for enumerating triangulations.
22 pages, 7 figures, 1 table. This version makes several changes based on feedback of the first version. This includes a change to the title and a new section with results on Erdős--Rényi random graphs