论文标题
在随机双曲线刺穿球体上的短大地测量学和小特征值
Short geodesics and small eigenvalues on random hyperbolic punctured spheres
论文作者
论文摘要
我们研究了Weil-Petersson随机属零双曲线表面上的简短大地测量学和小型特征值的数量，并在政权$ n \ to \ infty $中使用$ n $ cusps。受mirzakhani和petri \ cite {mi.pe19}的作品的启发，我们表明，在合适的重新恢复后，封闭的大地测量学的长度随机多组收敛到具有明显强度的Poisson点过程。结果，我们表明，Weil-Petersson的概率是$ n $ cusps的双曲线穿刺球至少具有$ k = o（n）$任意小的特征值往往为$ 1 $，为$ n \ to \ infty $。
We study the number of short geodesics and small eigenvalues on Weil-Petersson random genus zero hyperbolic surfaces with $n$ cusps in the regime $n\to\infty$. Inspired by work of Mirzakhani and Petri \cite{Mi.Pe19}, we show that the random multi-set of lengths of closed geodesics converges, after a suitable rescaling, to a Poisson point process with explicit intensity. As a consequence, we show that the Weil-Petersson probability that a hyperbolic punctured sphere with $n$ cusps has at least $k=o(n)$ arbitrarily small eigenvalues tends to $1$ as $n\to\infty$.
