AI 中文总结
本研究证明均匀随机不可分平面图的标度极限为布朗球面，提出非双射公共核转移方法这一通用证明策略，并完善了块加权平面图极限形状的相图。
AI 中文摘要
我们证明，具有$n$条边的均匀随机不可分平面图在$n$趋于无穷时，以布朗球面为其Gromov–Hausdorff–Prokhorov标度极限。我们的证明提出了一种非双射的“公共核转移方法”，为随机离散结构的标度极限研究提供了一种新颖且通用的证明策略。作为应用，我们完善了Stufler（2019）提出的块加权平面图极限形状的相图，描述了极限分别为布朗球面、稳定树，以及Sénizergues、Stefánsson与Stufler（2023）最新提出的布朗球面装饰稳定树的各相态。
英文摘要
We prove that the uniform random non-separable planar map with $n$ edges admits the Brownian sphere as Gromov--Hausdorff--Prokhorov scaling limit as $n$ tends to infinity. Our proof introduces a non-bijective ``common-core transfer method'' that constitutes a novel and universal proof strategy for scaling limits of random discrete structures. As an application, we complete the phase diagram for limiting shapes of block-weighted planar maps by Stufler~(2019). We describe phases with limits given by the Brownian sphere, stable trees, and Brownian sphere decorated stable trees recently introduced by S{é}nizergues, Stef{á}nsson and Stufler~(2023).
