点过程的Patterson-Sullivan测度与调和函数的重构
Patterson-Sullivan measures for point processes and the reconstruction of harmonic functions
摘要：
证明了Patterson-Sullivan构造几乎必然能从圆盘上高斯解析函数的零点集上的值恢复出一定巴拿赫空间中的每个调和函数.该论点依赖于有关点过程的线性统计量的方差增长缓慢。作为一般抽象背景下重构结果的推论，在任意维数的实和复双曲空间中得到了调和函数的Patterson-Sullivan重构.
英文摘要：
The Patterson-Sullivan construction is proved almost surely to recover every harmonic function in a certain Banach space from its values on the zero set of a Gaussian analytic function on the disk. The argument relies on the slow growth of variance for linear statistics of the concerned point process. As a corollary of reconstruction result in general abstract setting, Patterson-Sullivan reconstruction of harmonic functions is obtained in real and complex hyperbolic spaces of arbitrary dimension.
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。
