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 the Gaussian limit for linear statistics over determinantal point processes on the union of two copies of ℝd when the correlation kernels are J-Hermitian translation-invariant.
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Acknowledgements
Yanqi Qiu was supported by National Natural Science Foundation of China (Grant Nos. Y7116335K1, 11801547 and 11688101). Kai Wang was supported by National Natural Science Foundation of China (Grant Nos. 11722102 and 12026250), Shanghai Technology Innovation Project (Grant No. 21JC1400800) and Laboratory of Mathematics for Nonlinear Science, Ministry of Education of China.
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Lin, Z., Qiu, Y. & Wang, K. Gaussian limit for determinantal point processes with J-Hermitian kernels. Sci. China Math. 66, 1359–1374 (2023). https://doi.org/10.1007/s11425-021-1977-x
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DOI: https://doi.org/10.1007/s11425-021-1977-x
Keywords
- determinantal point process
- J-Hermitian kernel
- linear statistics
- central limit theorem
- translation-invariant kernel