25 citations · 57 across the 12 of their papers we have counts for
6 papers · 1 filter
Typical hyperbolic surfaces have a spectral gap greater than
Nalini Anantharaman, Laura Monk
In this article, we prove that typical hyperbolic surfaces, sampled with the Weil-Petersson probability measure, have a spectral gap at least . This is an intermediate res…
Typical hyperbolic surfaces have an optimal spectral gap
Laura Monk
The first non-zero Laplace eigenvalue of a hyperbolic surface, or its spectral gap, measures how well-connected the surface is: surfaces with a large spectral gap are hard to cut i…
Spectral Gaps on Large Hyperbolic Surfaces
Laura Monk, Frédéric Naud
In this expository paper, we review the history and the recent breakthroughs in the spectral theory of large volume hyperbolic surfaces. More precisely, we focus mostly on the inve…
The moduli space of twisted Laplacians and random matrix theory
Jens Marklof, Laura Monk
Rudnick recently proved that the spectral number variance for the Laplacian of a large compact hyperbolic surface converges, in a certain scaling limit and when averaged with respe…
Spectral convergence of the Dirac operator on typical hyperbolic surfaces of high genus
Laura Monk, Rares Stan
In this article, we study the Dirac spectrum of typical hyperbolic surfaces of finite area, equipped with a nontrivial spin structure (so that the Dirac spectrum is discrete). For…
Friedman-Ramanujan functions in random hyperbolic geometry and application to spectral gaps I
Nalini Anantharaman, Laura Monk
In this series of articles, we analyse the level-sets of length functions on the moduli space of compact hyperbolic surfaces of fixed genus. This work ultimately culminates in a pr…