随机弦图中极限定理的收敛速度
Convergence rates of limit theorems in random chord diagrams
摘要：
研究了随机弦图中交叉数和单弦数的渐近分布。利用尺寸偏差耦合和Stein的方法，我们得到了交叉数分布与标准正态随机变量之间的Kolmogorov距离和单弦数分布与Poisson随机变量之间的全变差距离的界.作为一个应用，我们提供了明确的误差界的弦图不包含简单的弦的数量。
英文摘要：
We study the asymptotic distributions of the number of crossings and the number of simple chords in a random chord diagram. Using size-bias coupling and Stein's method, we obtain bounds on the Kolmogorov distance between the distribution of the number of crossings and a standard normal random variable, and on the total variation distance between the distribution of the number of simple chords and a Poisson random variable. As an application, we provide explicit error bounds on the number of chord diagrams containing no simple chords.
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