Spectral Gap for Weil–Petersson Random Surfaces with Cusps

Hide, Will

Abstract

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.

Citation

Hide, W. (2022). Spectral Gap for Weil–Petersson Random Surfaces with Cusps. International Mathematics Research Notices, https://doi.org/10.1093/imrn/rnac293

• 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
• DOI: https://doi.org/10.1093/imrn/rnac293