Skip to main content

Research Repository

Advanced Search

Spectral Gap for Weil–Petersson Random Surfaces with Cusps

Hide, Will

Spectral Gap for Weil–Petersson Random Surfaces with Cusps Thumbnail



We show that for any ε>0⁠, α∈[0, 1 2 )⁠, as g→∞ a generic finite-area genus g hyperbolic surface with n=O(gα) cusps, sampled with probability arising from the Weil–Petersson metric on moduli space, has no non-zero eigenvalue of the Laplacian below 1 4 −( 2α+1 4 )2−ε⁠. For α=0 this gives a spectral gap of size 3 16 −ε and for any α< 1 2 gives a uniform spectral gap of explicit size.


Hide, W. (2022). Spectral Gap for Weil–Petersson Random Surfaces with Cusps. International Mathematics Research Notices,

Journal Article Type Article
Acceptance Date Oct 3, 2022
Online Publication Date Oct 20, 2022
Publication Date 2022
Deposit Date Jan 4, 2023
Publicly Available Date Jan 4, 2023
Journal International Mathematics Research Notices
Print ISSN 1073-7928
Electronic ISSN 1687-0247
Publisher Oxford University Press
Peer Reviewed Peer Reviewed


Published Journal Article (477 Kb)

Publisher Licence URL

Copyright Statement
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

You might also like

Downloadable Citations