论文标题
随机停车功能的循环结构
Cycle structure of random parking functions
论文作者
论文摘要
我们启动统一随机停车功能的循环结构的研究。使用停车场完成的组合，我们计算任何固定长度的循环数的渐近期望值。我们使用可交换对的Stein方法的多元版本的循环计数的关节分布与独立泊松随机变量之间的总变化距离获得了上限。在温和的条件下，周期计数的过程在分布中收敛到独立泊松随机变量的过程。
We initiate the study of the cycle structure of uniformly random parking functions. Using the combinatorics of parking completions, we compute the asymptotic expected value of the number of cycles of any fixed length. We obtain an upper bound on the total variation distance between the joint distribution of cycle counts and independent Poisson random variables using a multivariate version of Stein's method via exchangeable pairs. Under a mild condition, the process of cycle counts converges in distribution to a process of independent Poisson random variables.
