随机loop树和具有指定大面的双色平面图的缩放极限
Scaling limits of random looptrees and bipartite plane maps with prescribed large faces
AI总结：
本文通过loop树框架统一了双色平面图与标记树的 bijection，研究了具有大面的随机loop树和图的缩放极限，扩展了之前无大面的研究。
摘要：
我们首先重新表述并统一了双色平面图与标记树之间的已知 bijection，采用loop树的正式ism，认为其更相关且技术上更简单，因为loop树的几何由深度优先行走（或Łukasiewicz路径）显式编码，而非树的高度或轮廓过程。然后我们构造了与任何无负跳的 càdlàg 路径相关的连续类比，并推导出若干不变原理。我们特别关注具有指定面度的均匀随机loop树和图，并在存在宏观面的情况下研究其缩放极限，这补充了之前无大面情况的研究。极限（沿子序列对于图）形成新的随机度量测度空间家族，与具有无负跳的可交换增量的过程相关，我们的结果扩展了之前关注布朗运动和稳定莱维桥的研究。
英文摘要：
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.
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