发表机构
Courant Institute, New York University（纽约大学柯朗数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明左边界长度为一的量子圆盘面积满足大偏差原理，通过共形焊接与配对树定律导出递归分解，并利用Hamilton--Jacobi方程确定速率函数。
AI 中文摘要
我们证明了一个关于两点标记、权重为$W$且左边界长度为一的量子圆盘面积的大偏差原理，其中$0<W<2$固定且$\gamma\downarrow0$，无需子序列限制。共形焊接与单块配对树定律给出独立的布朗块与递归面积分解。增长矩与负拉普拉斯变换导出两个Hamilton--Jacobi方程，其特征解决定极限变换。直接比较证明矩收敛；紧区间比较与测度变换证明拉普拉斯收敛。所得良好速率函数由标量端点方程指定，且在$W=1$时为初等函数。
英文摘要
We prove a large deviation principle for the area of a two-pointed weight-$W$ quantum disk conditioned to have left boundary length one, where $0<W<2$ is fixed and $γ\downarrow0$ without a subsequence restriction. Conformal welding and the one-block mating-of-trees law give independent Brownian blocks and a recursive area decomposition. Growing moments and negative Laplace transforms lead to two Hamilton--Jacobi equations, whose characteristic solutions determine the limiting transforms. Direct comparison proves moment convergence; compact-interval comparison and a change of measure prove Laplace convergence. The resulting good rate function is specified by scalar endpoint equations and is elementary when $W=1$.
