论文标题
连接不变的随机排列中单词的小循环结构
Small cycle structure for words in conjugation invariant random permutations
论文作者
论文摘要
我们研究了几个随机排列中单词的循环结构。我们假设排列是独立的，它们的分布是共轭不变的，可以很好地控制其短周期。如果经过连续的循环简化后，w这个词仍然至少包含两个不同的字母，那么我们将获得一个普遍的限制联合定律，用于在这些排列中的单词。这些结果可以看作是我们先前的工作[Kammoun和Maïda，2020]的扩展，从排列的产物到排列中的任何非平凡单词，也是[NICA，1994]的结果从统一排列到一般共轭不变的随机排列的结果。
We study the cycle structure of words in several random permutations. We assume that the permutations are independent and that their distribution is conjugation invariant, with a good control on their short cycles. If, after successive cyclic simplifications, the word w still contains at least two different letters, then we get a universal limiting joint law for small cycles for the word in these permutations. These results can be seen as an extension of our previous work [Kammoun and Maïda, 2020] from the product of permutations to any non-trivial word in the permutations and also as an extension of the results of [Nica, 1994] from uniform permutations to general conjugation invariant random permutations.
