A survey of recent results proving that random hyperbolic surfaces of large genus have near-optimal spectral gaps, after Hide–Magee, Anantharaman–Monk, and Hide–Macera–Thomas.
Random surfaces with large systoles
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abstract
We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their area. This also allows us to prove a new lower bound on the maximal systole of a closed orientable hyperbolic surface of a given genus.
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Bass notes of random hyperbolic surfaces of large genus
A survey of recent results proving that random hyperbolic surfaces of large genus have near-optimal spectral gaps, after Hide–Magee, Anantharaman–Monk, and Hide–Macera–Thomas.