论文标题
大属双曲线表面上随机多晶的长度分区
Length partition of random multicurves on large genus hyperbolic surfaces
论文作者
论文摘要
我们研究了在$ g \ geq 2 $属表面上随机多晶的成分的长度统计。对于每个固定属，此类统计数据的存在遵循M.〜irzakhani，F。〜Arana-Herrera和M.〜liu的工作。我们证明，随着属$ g $的属倾向于无限统计，统计数据将法律汇合到Poisson- dirichlet分布$θ= 1/2 $。特别是，由于该属倾向于无穷大，三个最长组件的平均长度分别收敛到$ 75.8 \％$，$ 17.1 \％\％$和$ 4.9 \％\％\％\％\％$。
We study the length statistics of the components of a random multicurve on a surface of genus $g \geq 2$. For each fixed genus, the existence of such statistics follows from the work of M.~Mirzakhani, F.~Arana-Herrera and M.~Liu. We prove that as the genus $g$ tends to infinity the statistics converge in law to the Poisson--Dirichlet distribution of parameter $θ=1/2$. In particular, as the genus tends to infinity the mean length of the three longest components converge respectively to $75.8\%$, $17.1\%$ and $4.9\%$ of the total length.
