Bass notes of random hyperbolic surfaces of large genus

Abstract

This is a Séminaire Bourbaki survey on spectral gaps of random hyperbolic surfaces. The first part of the text is a brief survey on the geometry and spectra of random hyperbolic surfaces. After this, we discuss the results by Hide-Magee, Anantharaman-Monk and Hide-Macera-Thomas on near optimal spectral gaps for random surfaces.

arXiv comment63 pages, 11 figures, Exposé number 1255