Abstract
We show that the Weil–Petersson probability that a random surface has first eigenvalue of the Laplacian less than goes to zero as the genus goes to infinity.
Funding Statement
During the preparation of this paper, the first author was partially supported by a NSERC Discovery Grant, and the second author was partially supported by a Clay Research Fellowship, NSF Grant DMS-1856155, and a Sloan Research Fellowship.
Acknowledgements
We thank Farrell Brumley, Andrew Granville, Rafe Mazzeo, Peter Sarnak, and Scott Wolpert for helpful conversations. We also especially thank Paul Apisa and the referees for detailed and helpful comments.
Citation
Michael Lipnowski. Alex Wright. "Towards optimal spectral gaps in large genus." Ann. Probab. 52 (2) 545 - 575, March 2024. https://doi.org/10.1214/23-AOP1657
Information
