Gaussian limit for determinantal point processes with J-Hermitian kernels

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 ℝ d wh...

Full description

Saved in:
Bibliographic Details
Published inScience China. Mathematics Vol. 66; no. 6; pp. 1359 - 1374
Main Authors Lin, Zhaofeng, Qiu, Yanqi, Wang, Kai
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.06.2023
Springer Nature B.V
Subjects
Applications of Mathematics
Central limit theorem
Kernels
Mathematics
Mathematics and Statistics
central limit theorem
60G55
linear statistics
translation-invariant kernel
30B20
determinantal point process
30H20
Hermitian kernel
Online AccessGet full text

Cover

More Information
Summary: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 ℝ d when the correlation kernels are J -Hermitian translation-invariant.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-021-1977-x