AI 中文总结
该研究针对随机多重集合排列的不动点数量问题，采用斯坦因方法开展分析，拓展了普通排列不动点数量的泊松近似相关结论。
AI 中文摘要
对于n个字母的普通排列，随机排列的不动点数量分布，当n→∞时，在总变差距离下趋近于泊松(1)分布，这一结论已广为人知。我们采用斯坦因方法（Stein's method），针对随机多重集合排列的不动点数量，得到了相关结果。
英文摘要
For ordinary permutations on $n$ letters, the distribution of the number of fixed points of random permutations is well known to approach the Poisson$(1)$ distribution in total variation distance as $n\to\infty$ super-exponentially quickly. We use Stein's method to get related results for the number of fixed points of random permutations of multisets. Given a sequence of multisets on $n$ letters whose expected number of fixed points converges to a constant $c$, we must have $c\geq 1$ and the distribution of number of fixed points converges to the ${\rm Poisson}(c)$ distribution as $n\to\infty$. If $c>1$, then the rate of convergence in total variation distance can be as slow as $n^{-1/2}$.
Comments13 pages, minor additions
