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Let $X$ be a closed, connected, oriented surface of genus $g$, with a hyperbolic metric chosen at random according to the Weil--Petersson measure on the moduli space of Riemannian metrics.
Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series
Atle Selberg · 1956
Earlier work this paper cites.
Über den ersten Eigenwert des Laplace-Operators auf kompakten Riemannschen Flächen
Heinz Huber · 1974
Earlier work this paper cites.
Geometry and Spectra of Compact Riemann Surfaces
Peter Buser · 1992
Earlier work this paper cites.
A proof of Alon’s second eigenvalue conjecture
Joel Friedman · 2003
Earlier work this paper cites.
Simple geodesics and Weil–Petersson volumes of moduli spaces of bordered Riemann surfaces
Maryam Mirzakhani · 2007
Earlier work this paper cites.
Growth of Weil–Petersson volumes and random hyperbolic surfaces of large genus
Maryam Mirzakhani · 2013
Earlier work this paper cites.
The Spectrum of Hyperbolic Surfaces
Nicolas Bergeron · 2016
Cited alongside, same era.
Lengths of closed geodesics on random surfaces of large genus
Maryam Mirzakhani and Bram Petri · 2019
Cited alongside, same era.
A new proof of Friedman’s second eigenvalue theorem and its extension to random lifts
Charles Bordenave · 2020
Cited alongside, same era.
Near optimal spectral gaps for hyperbolic surfaces
Will Hide and Michael Magee · 2021
Cited alongside, same era.
Towards optimal spectral gaps in large genus
Michael Lipnowski and Alex Wright · 2021
Cited alongside, same era.
The tangle-free hypothesis on random hyperbolic surfaces
Laura Monk and Joe Thomas · 2021
Cited alongside, same era.
A high-genus asymptotic expansion of Weil–Petersson volume polynomials
Nalini Anantharaman and Laura Monk · 2022
Later among the works it cites.
Random hyperbolic surfaces of large genus have first eigenvalues greater than 3 16 − ϵ \frac{3}{16}-\epsilon
Yunhui Wu and Yuhao Xue · 2022
Later among the works it cites.
Friedman–Ramanujan functions in random hyperbolic geometry and application to spectral gaps
Nalini Anantharaman and Laura Monk · 2023
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Friedman–Ramanujan functions in random hyperbolic geometry and application to spectral gaps II
Nalini Anantharaman and Laura Monk · 2024
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A Moebius inversion formula to discard tangled hyperbolic surfaces
Nalini Anantharaman and Laura Monk · 2024
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