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.

中文翻译：

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大亏格双曲曲面的简单分离系统

在这篇文章中，我们展示了亏格g的随机曲面​​的分离收缩期相对于 Weil-Petersson 体积的预期值，随着亏格趋于无穷大，其行为类似于 $2\log g $ 。这与收缩期期望值的行为形成鲜明对比，根据 Mirzakhani 和 Petri 的结果，收缩期期望值独立于属。