Nearly optimal spectral gaps for random Belyi surfaces
Spectral Theory
2026-02-27 v2 Differential Geometry
Geometric Topology
Representation Theory
Abstract
In this paper, we show that a random hyperbolic surface in the Brooks-Makover model has a spectral gap greater than , confirming the nearly optimal spectral gap conjecture in this model.
Keywords
Cite
@article{arxiv.2511.02517,
title = {Nearly optimal spectral gaps for random Belyi surfaces},
author = {Yang Shen and Yunhui Wu},
journal= {arXiv preprint arXiv:2511.02517},
year = {2026}
}
Comments
46 pages, 9 figures, extend $\epsilon$ to $\left(\frac{1}{n}\right)^{\frac{1}{221}}\right)$ and provide certain new Ramanujan surfaces