论文标题
平面确定点过程平滑统计的正态性
Normality of smooth statistics for planar determinantal point processes
论文作者
论文摘要
我们考虑了复杂平面上确定点过程的平滑线性统计及其大规模渐进性。在有限差异案例中，我们证明了渐近态性，而Soshnikov的定理不适用。该设置类似于Rider和Virág[Electron。 J. Probab。，12，否。对于复杂平面的45，1238--1257，（2007）]，但通过假设相关内核正在再现。我们的证明是Ameur，Hedenmalm和Makarov的简化版本[Duke Math J.，159，31--81，（2011）]，用于正常随机矩阵的特征值。在我们的情况下，繁殖特性被带来以弥补缺乏分析性和径向对称性。
We consider smooth linear statistics of determinantal point processes on the complex plane, and their large scale asymptotics. We prove asymptotic normality in the finite variance case, where Soshnikov's theorem is not applicable. The setting is similar to that of Rider and Virág [Electron. J. Probab., 12, no. 45, 1238--1257, (2007)] for the complex plane, but replaces analyticity conditions by the assumption that the correlation kernel is reproducing. Our proof is a streamlined version of that of Ameur, Hedenmalm and Makarov [Duke Math J., 159, 31--81, (2011)] for eigenvalues of normal random matrices. In our case, the reproducing property is brought to bear to compensate for the lack of analyticity and radial symmetries.
