English

Towards optimal spectral gaps in large genus

Geometric Topology 2023-07-20 v3 Number Theory Probability Spectral Theory

Abstract

We show that the Weil-Petersson probability that a random surface has first eigenvalue of the Laplacian less than 3/16ϵ3/16-\epsilon goes to zero as the genus goes to infinity.

Cite

@article{arxiv.2103.07496,
  title  = {Towards optimal spectral gaps in large genus},
  author = {Michael Lipnowski and Alex Wright},
  journal= {arXiv preprint arXiv:2103.07496},
  year   = {2023}
}

Comments

35 pages. Comments welcome. v3: Revisions based on referee comments

R2 v1 2026-06-24T00:05:06.135Z