Random growth on a Ramanujan graph
Combinatorics
2019-10-23 v2 Discrete Mathematics
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 Erd\H{o}s--R\'enyi random graphs and compare our theoretical results with computational experiments on flip graphs of point configurations. The latter is relevant for enumerating triangulations.
Cite
@article{arxiv.1908.09575,
title = {Random growth on a Ramanujan graph},
author = {Janko Boehm and Michael Joswig and Lars Kastner and Andrew Newman},
journal= {arXiv preprint arXiv:1908.09575},
year = {2019}
}
Comments
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 Erd\H{o}s--R\'{e}nyi random graphs