标题： 关于球面上确定性点过程的对相关统计量 显示英文标题

标题： On the pair correlation statistics for determinantal point processes on the sphere

摘要： 在本文中，我们研究了球面上随机点配置的对相关统计量的期望值，重点研究由确定性点过程生成的点配置。我们研究了球面系综、谐波系综和抖动采样的情况，并将我们的结果与“真正随机”（独立同分布）的情况进行比较。我们的结果提供了确定性点过程特有的小尺度排斥现象的证据，而在较大尺度上，我们研究的所有情况与独立同分布的情况有很好的一致性。 显示英文摘要

摘要： In this paper, we study the expected value of the pair correlation statistics of randomized point configurations on the sphere, with the emphasis on point configurations generated by determinantal point processes. We study the cases of the spherical ensemble, the harmonic ensemble, and jittered sampling, and compare our results with those for the ''truly random'' (i.i.d.) case. Our results give evidence of the small-scale repulsion phenomenon which is characteristic for determinantal point processes, while on larger scales there is good agreement between all our studied cases and the i.i.d. case.