Nearly optimal spectral gaps for random Belyi surfaces

2025/11/04 by Shen, Yang, Wu, Yunhui · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Representation Theory (math.RT) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2511.02517

Abstract

In this paper, we show that for any ε>0, a random hyperbolic surface in the Brooks-Makover model has a spectral gap greater than (1)/(4)-ε, confirming the nearly optimal spectral gap conjecture in this model.

Citations

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Cited by

• Apollonian random manifolds and their bass notes

Related

• Spectral gap of random hyperbolic surfaces
• Spectral gap with polynomial rate for random covering surfaces
• Near optimal spectral gaps for hyperbolic surfaces
• Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps
• Spectral gap with polynomial rate for Weil-Petersson random surfaces