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arXiv · 2511.02517

Nearly optimal spectral gaps for random Belyi surfaces

Yang Shen·Yunhui Wu
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Abstract

In this paper, we show that a random hyperbolic surface in the Brooks-Makover model has a spectral gap greater than $\left(\frac{1}{4}-\frac{c}{\log n}\right)$ for some universal constant $c>0$ , confirming the nearly optimal spectral gap conjecture in this model.

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Yang Shen, Yunhui Wu. 2026-06-09. Nearly optimal spectral gaps for random Belyi surfaces. https://arxiv.org/abs/2511.02517

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