5 citations · 6 across the 10 of their papers we have counts for
11 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 .
Small eigenvalues of hyperbolic surfaces with many cusps
Will Hide, Joe Thomas
We study topological lower bounds on the number of small Laplacian eigenvalues on hyperbolic surfaces. We show that for any , there exists such that if and ha…
Large- asymptotics for Weil-Petersson volumes of moduli spaces of bordered hyperbolic surfaces
Will Hide, Joe Thomas
We study the geometry and spectral theory of Weil-Petersson random surfaces with genus- and cusps in the large- limit. We show that for a random hyperbolic surface in $\m…
Effective lower bounds for spectra of random covers and random unitary bundles
Will Hide
Let be a finite-area non-compact hyperbolic surface. We study the spectrum of the Laplacian on random covering surfaces of X and on random unitary bundles over X. We show that…
Short geodesics and small eigenvalues on random hyperbolic punctured spheres
Will Hide, Joe Thomas
We study the number of short geodesics and small eigenvalues on Weil-Petersson random genus zero hyperbolic surfaces with cusps in the regime . Inspired by work of…
Spectral gap for Weil-Petersson random surfaces with cusps
Will Hide
We show that for any , , as a generic finite-area genus g hyperbolic surface with cusps, sampled with probability arisi…
Near optimal spectral gaps for hyperbolic surfaces
Will Hide, Michael Magee
We prove that if is a finite area non-compact hyperbolic surface, then for any , with probability tending to one as , a uniformly random degree Riemannian…