Typical hyperbolic surfaces under the Weil-Petersson measure have spectral gap at least 2/9 - ε.
A proof of Alon’s second eigenvalue conjecture.Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, pages 720–724
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Typical hyperbolic surfaces have a spectral gap greater than $2/9 - \epsilon$
Typical hyperbolic surfaces under the Weil-Petersson measure have spectral gap at least 2/9 - ε.