Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality
Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality
复制标题
DOI：
10.1007/s10955-017-1928-2
复制
发表时间：
2016-03
影响因子：
1.6
通讯作者：
H. Osada;Shota Osada
中科院分区：
文献类型：
--
作者：
H. Osada;Shota Osada
We prove tail triviality of determinantal point processeson continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for, and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.
