Length spectrum of large genus random metric maps
Probability
2025-04-16 v1 Combinatorics
Geometric Topology
Abstract
We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichm\"uller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a Poisson point process with an explicit intensity. This result extends the work of Janson and Louf to the multi-faced case.
Cite
@article{arxiv.2312.10517,
title = {Length spectrum of large genus random metric maps},
author = {Simon Barazer and Alessandro Giacchetto and Mingkun Liu},
journal= {arXiv preprint arXiv:2312.10517},
year = {2025}
}
Comments
28 pages