The simple separating systole for hyperbolic surfaces of large genus

Abstract

In this note we show that the expected value of the separating systole of a random surface of genus $g$ with respect to Weil-Petersson volume behaves like $2\log g$ 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.

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