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Nearly optimal spectral gaps for random Belyi surfaces

Published 4 Nov 2025 in math.SP, math.DG, math.GT, and math.RT | (2511.02517v1)

Abstract: In this paper, we show that for any $\epsilon>0$, a random hyperbolic surface in the Brooks-Makover model has a spectral gap greater than $\frac{1}{4}-\epsilon$, confirming the nearly optimal spectral gap conjecture in this model.

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