树根地图的相变
Phase transition for tree-rooted maps
AI总结：
本文引入以 $2$-连通块数量为权重的树根平面地图模型，证明其经历相变，给出了三种状态下最大 $2$-连通块大小的分布，并确定了临界与超临界状态下的缩放极限为 Brownian Continuum Random Tree。
摘要：
我们引入了一个以 $2$-连通块数量为权重的树根平面地图模型。我们研究了其计数性质并证明它经历了一次相变。我们给出了在三种状态（亚临界、临界和超临界）下最大 $2$-连通块大小的分布，并进一步证明在临界和超临界状态下，缩放极限均为 Brownian Continuum Random Tree，其重标度分别为 $\sqrt{n/\log(n)}$ 和 $\sqrt{n}$。
英文摘要：
We introduce a model of tree-rooted planar maps weighted by their number of $2$-connected blocks. We study its enumerative properties and prove that it undergoes a phase transition. We give the distribution of the size of the largest $2$-connected blocks in the three regimes (subcritical, critical and supercritical) and further establish that the scaling limit is the Brownian Continuum Random Tree in the critical and supercritical regimes, with respective rescalings $\sqrt{n/\log(n)}$ and $\sqrt{n}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
