Typical hyperbolic surfaces have a spectral gap greater than $2/9 - \epsilon$
Spectral Theory
2026-04-14 v1
Abstract
In this article, we prove that typical hyperbolic surfaces, sampled with the Weil-Petersson probability measure, have a spectral gap at least . This is an intermediate result on the way to our proof of the optimal spectral gap , building on the results of the first part of this series. A significant part of the proof is an explicit inclusion-exclusion argument to exclude tangles at the level of precision .
Keywords
Cite
@article{arxiv.2604.09792,
title = {Typical hyperbolic surfaces have a spectral gap greater than $2/9 - \epsilon$},
author = {Nalini Anantharaman and Laura Monk},
journal= {arXiv preprint arXiv:2604.09792},
year = {2026}
}
Comments
22 pages. The content of this article used to be the last section of arxiv:2304.02678, which we have now split into two articles. The contents are otherwise unchanged