发表机构
Courant Institute, New York University（纽约大学柯朗研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明 mated-CRT 映射在圆填充和黎曼均匀化嵌入下收敛于刘维尔量子引力，并推广了 He-Schramm 的收敛结果，为后续生成树加权平面映射的收敛奠定基础。
AI 中文摘要
我们证明了 mated-CRT 映射在圆填充和黎曼均匀化嵌入下收敛于刘维尔量子引力。该证明基于我们近期关于随机平面映射在遍历尺度自由环境中的圆填充与黎曼均匀化嵌入的工作、不同区域中圆填充的比较，以及针对 mated-CRT 映射的若干现有和新的估计。作为中间步骤，我们在若干设置下将 He 和 Schramm（1996）关于圆填充映射收敛于共形映射的结果推广到全局一致拓扑。后者具有独立意义，并将应用于我们后续关于生成树加权平面映射在圆填充和黎曼均匀化嵌入下收敛于 $\sqrt{2}$-LQG 的工作。
英文摘要
We prove that the mated-CRT map converges to Liouville quantum gravity under circle packing and the Riemann uniformization embedding. The proof is based on our recent work on circle packing and the Riemann uniformization embedding for random planar maps in ergodic-scale free environments, comparison of circle packing in different domains and several existing and new estimates for the mated-CRT map. As an intermediate step, we prove an extension of He and Schramm's result (1996) on convergence of circle packing maps to conformal maps to global uniform topology in several settings. The latter results are of independent interest and will be applied in our subsequent work on the convergence of spanning tree weighted planar maps to $\sqrt{2}$-LQG under circle packing and Riemann uniformization embedding.
Comments47 pages, 9 figures
