Typical hyperbolic surfaces under the Weil-Petersson measure have spectral gap at least 2/9 - ε.
Random hyperbolic surfaces of large genus have first eigenvalues greater than 3 16 −ϵ.Geometric and Functional Analysis, 32(2):340–410, 2022
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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.