论文标题
随机循环的缩放限制和带有大面的二分平面图
Scaling limits of random looptrees and bipartite plane maps with prescribed large faces
论文作者
论文摘要
我们首先重现并统一了两分平面映射的已知徒和带有循环形式的树木之间的已知徒，我们认为我们既相关又技术上更简单，因为looptree的几何形状是由深度 - 段（或a lukaukasiew path）（或coulukasiew path）明确编码的。然后，我们构建与任何Càdlàg路径相关的连续类似物，没有负跳跃，并得出了几个不变性原则。我们特别关注具有规定的面部度的统一随机循环和地图，并在存在宏观面孔的情况下研究其缩放限制，这在没有大面孔的情况下可以补充先前的工作。限制（沿着地图的子序列）形成了与随机度量的空间的新家族，与可交换增量相关的过程，没有负跳跃，我们的结果概括了以前的工作，这与布朗和稳定的lévybridges有关。
We first rephrase and unify known bijections between bipartite plane maps and labelled trees with the formalism of looptrees, which we argue to be both more relevant and technically simpler since the geometry of a looptree is explicitly encoded by the depth-first walk (or Łukasiewicz path) of the tree, as opposed to the height or contour process for the tree. We then construct continuum analogues associated with any càdlàg path with no negative jump and derive several invariance principles. We especially focus on uniformly random looptrees and maps with prescribed face degrees and study their scaling limits in the presence of macroscopic faces, which complements a previous work in the case of no large faces. The limits (along subsequences for maps) form new families of random metric measured spaces related to processes with exchangeable increments with no negative jumps and our results generalise previous works which concerned the Brownian and stable Lévy bridges.
