论文标题
仿生集合：与AX+B组相关的确定点过程
The affine ensemble: determinantal point processes associated with the ax+b group
论文作者
论文摘要
我们介绍了与AX+ B（Aggine）组相关的半平面C^+中的一类确定点过程（DPP），具体取决于可接受的Hardy函数ψ。我们获得了方差的渐近行为，渐近常数的确切值以及在C^+中包含的紧凑型集合ω上的方差的非质子上限和下限。作为特殊情况，人们恢复了与加权伯格曼内核有关的DPP。当在一个有限的家族中选择ψ时，其傅立叶变换是拉瓜尔的函数时，我们获得了与双曲线兰道水平相关的DPP，这是Maass Laplacian的有限频谱的特征区，并带有磁场。
We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C^+ associated with the ax+b (affine) group, depending on an admissible Hardy function ψ. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set Ω contained in C^+. As a special case one recovers the DPP related to the weighted Bergman kernel. When ψ is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.
