论文标题
随机毁灭和EWENS采样公式
Random derangements and the Ewens Sampling Formula
论文作者
论文摘要
我们研究了带有参数$θ$的ewens分发下的$ \ {1,2，\ ldots，n \} $的扰动。我们给出了周期计数的时刻和边际分布，周期的数量和大型$ n $的渐近分布。我们开发了一个$ \ {0,1 \} $ - 有价值的非均匀马尔可夫链，其属性具有1S之间间距长度的属性，具有毁灭性分布。该链是所谓的feller耦合的类似物，它提供了一种简单的方法，可以在给定的$ n $的$θ$中及时模拟扰动，并在扰动大小的情况下进行线性。
We study derangements of $\{1,2,\ldots,n\}$ under the Ewens distribution with parameter $θ$. We give the moments and marginal distributions of the cycle counts, the number of cycles, and asymptotic distributions for large $n$. We develop a $\{0,1\}$-valued non-homogeneous Markov chain with the property that the counts of lengths of spacings between the 1s have the derangement distribution. This chain, an analog of the so-called Feller Coupling, provides a simple way to simulate derangements in time independent of $θ$ for a given $n$ and linear in the size of the derangement.
