Gaussian limit for determinantal point processes with $J$-Hermitian kernels

Zhaofeng Lin; Yanqi Qiu; Kai Wang

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arXiv · 2101.00384

Gaussian limit for determinantal point processes with $J$-Hermitian kernels

Zhaofeng Lin·Yanqi Qiu·Kai Wang

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Abstract

We show that the central limit theorem for linear statistics over determinantal point processes with $J$-Hermitian kernels holds under fairly general conditions. In particular, We establish Gaussian limit for linear statistics over determinantal point processes on union of two copies of $\mathbb{R}^d$ when the correlation kernels are $J$-Hermitian translation-invariant.

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Zhaofeng Lin, Yanqi Qiu, Kai Wang. 2021-01-02. Gaussian limit for determinantal point processes with $J$-Hermitian kernels. https://arxiv.org/abs/2101.00384

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