Title: The permuton limit of random recursive separable permutations Show Chinese title

Title: 递归可分排列的排列图极限

Abstract: We introduce and study a simple Markovian model of random separable permutations. Our first main result is the almost sure convergence of these permutations towards a random limiting object in the sense of permutons, which we call the recursive separable permuton. We then prove several results on this new limiting object: a characterization of its distribution via a fixed-point equation, a combinatorial formula for its expected pattern densities, an explicit integral formula for its intensity measure, and lastly, we prove that its distribution is absolutely singular with respect to that of the Brownian separable permuton, which is the large size limit of uniform random separable permutations. Show Chinese abstract

Abstract: 我们引入并研究了一个简单的马尔可夫随机可分离排列模型。 我们的第一个主要结果是这些排列在排列子意义下几乎必然收敛到一个随机极限对象，我们称之为递归可分离排列子。 然后我们证明了这个新的极限对象的几个结果：通过一个固定点方程对其分布的描述，其期望模式密度的组合公式，其强度测度的显式积分公式，最后，我们证明了其分布相对于布朗可分离排列子是绝对奇异的，后者是均匀随机可分离排列在大尺寸下的极限。