English

The simple separating systole for hyperbolic surfaces of large genus

Geometric Topology 2021-07-01 v3 Differential Geometry

Abstract

In this note we show that the expected value of the separating systole of a random surface of genus gg with respect to Weil-Petersson volume behaves like 2logg2\log g as the genus goes to infinity. This is in strong contrast to the behavior of the expected value of the systole which, by results of Mirzakhani and Petri, is independent of genus.

Keywords

Cite

@article{arxiv.2012.03718,
  title  = {The simple separating systole for hyperbolic surfaces of large genus},
  author = {Hugo Parlier and Yunhui Wu and Yuhao Xue},
  journal= {arXiv preprint arXiv:2012.03718},
  year   = {2021}
}

Comments

9 pages. Journal of the Institute of Mathematics of Jussieu, to appear