Towards optimal spectral gaps in large genus

2021/03/12 by Lipnowski, Michael, Wright, Alex · 6 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT) #Probability (math.PR) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2103.07496

Abstract

We show that the Weil-Petersson probability that a random surface has first eigenvalue of the Laplacian less than 3/16-ε goes to zero as the genus goes to infinity.

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• Shortest filling geodesics on hyperbolic surfaces
• The tight length spectrum of large-genus random hyperbolic surfaces with many cusps

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