论文标题
随机标记树中交叉数的收敛率
Convergence Rate for The Number of Crossing in a Random Labelled Tree
论文作者
论文摘要
我们考虑具有凸位位置的带顶点的随机标记树中的交叉数。我们给出了一个新的证明，证明此数量是渐近高斯，平均$ n^2/6 $和方差$ n^3/45 $。此外，我们将kolmogorov距离的估算值估算到高斯分布，这意味着订单的收敛速率$ n^{ - 1/2} $。
We consider the number of crossings in a random labelled tree with vertices in convex position. We give a new proof of the fact that this quantity is asymptotically Gaussian with mean $n^2/6$ and variance $n^3/45$. Furthermore, we give an estimate for the Kolmogorov distance to a Gaussian distribution which implies a convergence rate of order $n^{-1/2}$.
