We consider uniform random permutations in proper substitution-closed classes and study their limiting behavior in the sense of permutons. The limit depends on the generating series of the simple permutations in the class. Under a mild sufficient condition, the limit is an elementary one-parameter deformation of the limit of uniform separable permutations, previously identified as the Brownian separable permuton. This limiting object is therefore in some sense universal. We identify two other regimes with different limiting objects. The first one is degenerate; the second one is nontrivial and related to stable trees. These results are obtained thanks to a characterization of the convergence of random permutons through the convergence of their expected pattern densities. The limit of expected pattern densities is then computed by using the substitution tree encoding of permutations and performing singularity analysis on the tree series.

中文翻译：

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替代封闭置换类的通用限制

我们在适当的替代封闭类中考虑均匀随机排列，并在排列的意义上研究它们的限制行为。限制取决于类中简单排列的生成序列。在温和的充分条件下，该极限是均匀可分离排列极限的基本单参数变形，之前被确定为布朗可分离排列。因此，这个限制对象在某种意义上是普遍的。我们确定了其他两种具有不同限制对象的制度。第一个是退化的；第二个是重要的，与稳定的树有关。这些结果是由于随机排列的收敛特征通过其预期模式密度的收敛而获得的。