基于标号树对称化的奇角剖分的收敛性
Convergence of odd-angulations via symmetrization of labeled trees
摘要：
将$p\geq 5$固定为奇数整数。设$M_n$是具有$n$顶点的均匀$p$ -角剖分，并赋予其顶点上的均匀概率测度.证明了存在$C_p\in \mathbb{R}_+$，使得当用$C_p/n^{1/4}$重新标度距离后，对于Gromov-Hausdorff-Prokhorov拓扑，$M_n$按分布收敛于布朗映射.为了证明上述事实，我们引入了随机标记平面树的分布收敛的“引导”原则。特别地，后者允许获得标记多型Galton-Watson树的不变原理，仅对标记位移的中心进行弱假设
英文摘要：
Fix $p\geq 5$ an odd integer integer. Let $M_n$ be a uniform $p$-angulation with $n$ vertices and endowed with the uniform probability measure on its vertices. We prove that, there exists $C_p\in \mathbb{R}_+$ such that, after rescaling distances by $C_p/n^{1/4}$, $M_n$ converges in distribution for the Gromov-Hausdorff-Prokhorov topology towards the Brownian map. To prove the preceding fact, we introduce a `bootstrapping' principle for distributional convergence of random labelled plane trees. In particular, the latter allows to obtain an invariance principle for labeled multitype Galton-Watson trees, with only a weak assumption on the centering of label displacements
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