6 citations · 6 across the 2 of their papers we have counts for
7 papers
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 re…
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…
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…
A Moebius inversion formula to discard tangled hyperbolic surfaces
Nalini Anantharaman, Laura Monk
Recent literature on Weil-Petersson random hyperbolic surfaces has met a consistent obstacle: the necessity to condition the model, prohibiting certain rare geometric patterns (whi…
Friedman-Ramanujan functions in random hyperbolic geometry and application to spectral gaps II
Nalini Anantharaman, Laura Monk
The core focus of this series of two articles is the study of the distribution of the length spectrum of closed hyperbolic surfaces of genus , sampled randomly with respect to t…