Nearly optimal spectral gaps for random Belyi surfaces

Yang Shen; Yunhui Wu

arxiv: 2511.02517 · v3 · pith:BKUS3MYTnew · submitted 2025-11-04 · 🧮 math.SP · math.DG· math.GT· math.RT

Nearly optimal spectral gaps for random Belyi surfaces

Yang Shen , Yunhui Wu This is my paper

classification 🧮 math.SP math.DGmath.GTmath.RT

keywords spectralfracmodelnearlyoptimalrandombelyibrooks-makover

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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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Nearly optimal spectral gaps for random Belyi surfaces

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