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
本研究证明在最大嵌入条带中，单位面积量子盘在γ趋于0时收敛到确定性场及其常曲率面积测度，通过联合大偏差原理和Girsanov平移等工具实现了浓度，无需二次展开，并将场速率与重整化Liouville作用量等同。
AI 中文摘要
固定$W\in(0,2)$并令$\gamma\downarrow0$。我们证明，在最大嵌入条带中，以单位量子面积为条件的权重为$W$的量子盘收敛到确定性场$\phi_W(t+i\theta)=\log(W/(4\pi))-2\log\cosh(Wt/2)$及其常曲率面积测度。该证明建立了径向布朗输入、侧向高斯自由场和总高斯乘法混沌质量的一个联合大偏差原理。发散阶矩界证明了将非连续面积泛函纳入单位面积期望并保留其无界正幂的合理性。一个精确的径向Girsanov平移使候选场居中，反射与尖锐的Onofri不等式共同证明了其唯一最优性。这实现了集中，而无需运行最大值的二次展开或一阶配分函数渐近。我们还将场速率与最大嵌入中的重整化Liouville作用量等同起来。
英文摘要
Fix $W\in(0,2)$ and let $γ\downarrow0$. We prove that a weight-$W$ quantum disk conditioned to have unit quantum area converges, in the maximum-embedded strip, to the deterministic field $ϕ_W(t+iθ)=\log(W/(4π))-2\log\cosh(Wt/2)$ and its constant-curvature area measure. The proof establishes a joint large-deviation principle for the radial Brownian input, the lateral Gaussian free field, and the total Gaussian multiplicative chaos mass. Diverging-order moment bounds justify both adjoining the noncontinuous area functional and retaining its unbounded positive power in the unit-area expectation. An exact radial Girsanov shift centers the candidate, and reflection together with the sharp Onofri inequality proves its unique optimality. This yields concentration without a quadratic expansion of the running maximum or an order-one partition-function asymptotic. We also identify the field rate with the renormalized Liouville action in the maximum embedding.
