论文标题
随机排列和其他一些组的通用性
Universality for random permutations and some other groups
论文作者
论文摘要
我们提出了一些马尔可夫的方法，以证明对称组的某些功能的普遍性结果。这些统计数据中的一些已经在[Kammoun，2018，2020]中进行了研究，但没有一般情况。我们尤其证明，围绕模式的发生数量满足了连接不变的随机排列的CLT，而循环很少，并且我们改善了由于最长增加的子序列而已知的结果。第二种方法是对其他随机排列的概括和与对称组相似的结构相似结构的建议。
We present some Markovian approaches to prove universality results for some functions on the symmetric group. Some of those statistics are already studied in [Kammoun, 2018, 2020] but not the general case. We prove, in particular, that the number of occurrences of a vincular patterns satisfies a CLT for conjugation invariant random permutations with few cycles and we improve the results already known for the longest increasing subsequence. The second approach is a suggestion of a generalization to other random permutations and other sets having a similar structure than the symmetric group.
