We prove Poisson approximation results for the bottom part of the length spectrum of a random closed hyperbolic surface of large genus. Here, a random hyperbolic surface is a surface picked at random using the Weil-Petersson volume form on the corresponding moduli space. As an application of our result, we compute the large genus limit of the expected systole.

中文翻译：

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大属随机曲面上闭合测地线的长度

我们证明了大属的随机闭合双曲曲面的长度谱底部的泊松近似结果。这里，随机双曲曲面是在相应的模空间上使用 Weil-Petersson 体积形式随机选取的曲面。作为我们结果的应用，我们计算了预期收缩期的大属极限。