投影 Hardy--Szegő 零点的 Palm 分解与高度剖面恢复
Palm Disintegration and Height-Profile Recovery for Projected Hardy--Szegő Zeros
- School of Mathematics, South China University of Technology（华南理工大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文研究上半平面 Hardy--Szegő 零点过程经高度相关稀疏化后的水平投影，通过 Palm 分解刻画投影过程条件律，并证明由投影二阶结构可唯一且 Lipschitz 稳定地恢复紧支撑高度测度。
中文摘要 AI 辅助
我们研究了上半平面 Hardy--Szegő 零点过程在独立的高度相关稀疏化后的水平投影，其中高度作为未观测的标记保留。我们通过对缺失的高度坐标进行分解来识别投影过程的约化 Palm 律，描述了与一对投影点相关的两个高度的条件分布及其近距和远距分离极限，并获得了右最近邻的小间距渐近性。然后，我们研究了从投影的二阶结构恢复高度剖面的问题。所得的协方差变换唯一地确定每个紧支撑的有限正高度测度，并且对于分离的有限区间并集，即使区间数量未知但有界，也能对所有端点实现均匀 Lipschitz 恢复。
英文摘要
We study the horizontal projection of the upper-half-plane Hardy--Szegő zero process after independent height-dependent thinning, with height retained as an unobserved mark. We identify the reduced Palm law of the projected process by disintegrating over the missing height coordinate, describe the conditional law of the two heights associated with a pair of projected points and its near- and far-separation limits, and obtain the small-spacing asymptotic for the right nearest neighbour. We then study recovery of the height profile from the projected second-order structure. The resulting covariance transform uniquely determines every compactly supported finite positive height measure and, for separated finite unions of intervals, yields uniform Lipschitz recovery of all endpoints, even when the number of intervals is unknown but bounded.
