Large expanders in high genus unicellular maps
Combinatorics
2021-02-26 v2 Probability
Abstract
We study large uniform random maps with one face whose genus grows linearly with the number of edges. They can be seen as a model of discrete hyperbolic geometry. In the past, several of these hyperbolic geometric features have been discovered, such as their local limit or their logarithmic diameter. In this work, we show that with high probability such a map contains a very large induced subgraph that is an expander.
Cite
@article{arxiv.2102.11680,
title = {Large expanders in high genus unicellular maps},
author = {Baptiste Louf},
journal= {arXiv preprint arXiv:2102.11680},
year = {2021}
}
Comments
18 pages, 8 figures (v2: minor error corrected)