5 papers
Apollonian random manifolds and their bass notes
Will Hide, Bram Petri, Anna Roig-Sanchis +1
We study the spectrum of the Laplacian on two models of random hyperbolic 3-orbifolds, related to the Apollonian group and the super Apollonian group. We determine explicit spectra…
Spectral gap with polynomial rate for Weil-Petersson random surfaces
Will Hide, Davide Macera, Joe Thomas
We show that there is a constant such that a genus closed hyperbolic surface, sampled at random from the moduli space with respect to the Weil-Petersson…
Spectral gap with polynomial rate for random covering surfaces
Will Hide, Davide Macera, Joe Thomas
In this note we show that the recent work of Magee, Puder and van Handel [MPvH25] can be applied to obtain an optimal spectral gap result with polynomial error rate for uniformly r…
On the spectral gap of negatively curved surface covers
Will Hide, Julien Moy, Frederic Naud
Given a negatively curved compact Riemannian surface , we give an explicit estimate, valid with high probability as the degree goes to infinity, of the first non-trivial eigenva…
Limit points of uniform arithmetic bass notes
Will Hide, Bram Petri
We prove that the set of limit points of the set of all spectral gaps of closed arithmetic hyperbolic surfaces equals .