Covariance of linear statistics of stationary random measures is expanded in terms of higher-order integrals of the truncated pair correlation measure, yielding variance asymptotics that skip alternate powers and surface-order asymptotics for indicator statistics.
Determinantal point processes on spheres: multivariate linear statistics
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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 $S^d$. 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.
fields
math.PR 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Stationary random measures : Covariance asymptotics, variance bounds and central limit theorems
Covariance of linear statistics of stationary random measures is expanded in terms of higher-order integrals of the truncated pair correlation measure, yielding variance asymptotics that skip alternate powers and surface-order asymptotics for indicator statistics.