English

Determinantal point processes on spheres: multivariate linear statistics

Probability 2023-01-24 v1

Abstract

In this paper, we will derive the first and 2nd order Wiener chaos decomposition for the multivariate linear statistics of the determinantal point processes associated with the spectral projection kernels on the unit spheres SdS^d. We will first get a graphical representation for the cumulants of multivariate linear statistics for any determinantal point process. The main results then follow from the very precise estimates and identities regarding the spectral projection kernels and the symmetry of the spheres.

Keywords

Cite

@article{arxiv.2301.09216,
  title  = {Determinantal point processes on spheres: multivariate linear statistics},
  author = {Renjie Feng and Friedrich Götze and Dong Yao},
  journal= {arXiv preprint arXiv:2301.09216},
  year   = {2023}
}
R2 v1 2026-06-28T08:17:27.251Z