On the Spectral Gap of the Laplacian for Random Hyperbolic Surfaces

 Although there are several ways to  »choose a compact hyperbolic surface at random », putting the Weil-Petersson probability measure on the moduli space of hyperbolic surfaces of a given topology is certainly the most natural.
The work of M. Mirzakhani has made possible the study of this probabilistic model: it is one of the only models of  »random Riemannian manifolds » where some explicit calculations are actually possible. One may thus ask questions about of the geometry and the spectral statistics of the Laplacian of a randomly chosen surface — in analogy with what is usually asked for models of random graphs.
I will be interested in the spectral gap of the Laplacian for a random compact hyperbolic surface, in the limit of large genus (joint work with Laura Monk).