25 citations · 57 across the 12 of their papers we have counts for
13 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 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…
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…
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 gap of random hyperbolic surfaces
Nalini Anantharaman, Laura Monk
Let be a closed, connected, oriented surface of genus , with a hyperbolic metric chosen at random according to the Weil--Petersson measure on the moduli space of Riemannian…
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…
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…
A high-genus asymptotic expansion of Weil-Petersson volume polynomials
Nalini Anantharaman, Laura Monk
The object under consideration in this article is the total volume of the moduli space of hyperbolic surfaces of genus with boundary components…
The tangle-free hypothesis on random hyperbolic surfaces
Laura Monk, Joe Thomas
This article introduces the notion of L-tangle-free compact hyperbolic surfaces, inspired by the identically named property for regular graphs. Random surfaces of genus g, picked w…
Benjamini-Schramm convergence and spectrum of random hyperbolic surfaces of high genus
Laura Monk
We study geometric and spectral properties of typical hyperbolic surfaces of high genus, excluding a set of small measure for the Weil-Petersson probability measure. We first prove…
Resonant thickening of self-gravitating discs: imposed or self-induced orbital diffusion in the tightly wound limit
Jean-Baptiste Fouvry, Christophe Pichon, Pierre-Henri Chavanis +1
The secular thickening of a self-gravitating stellar galactic disc is investigated using the dressed collisionless Fokker-Planck equation and the inhomogeneous multicomponent Bales…