Determinantal point process models on the sphere

Research output: Contribution to journalJournal articleResearchpeer-review

15 Citations (Scopus)

Abstract

We consider determinantal point processes on the d-dimensional unit sphere S d . These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified by a so-called kernel which we assume is a complex covariance function defined on S d ×S d. We review the appealing properties of such processes, including their specific moment properties, density expressions and simulation procedures. Particularly, we characterize and construct isotropic DPPs models on S d , where it becomes essential to specify the eigenvalues and eigenfunctions in a spectral representation for the kernel, and we figure out how repulsive isotropic DPPs can be. Moreover, we discuss the shortcomings of adapting existing models for isotropic covariance functions and consider strategies for developing new models, including a useful spectral approach.

Original languageEnglish
JournalBernoulli
Volume24
Issue number2
Pages (from-to)1171-1201
Number of pages31
ISSN1350-7265
DOIs
Publication statusPublished - May 2018

Keywords

  • isotropic covariance function
  • joint intensities
  • quantifying repulsiveness
  • Schoenberg representation
  • spatial point process density
  • spectral representation
  • Isotropic covariance function
  • Quantifying repulsiveness
  • Spatial point process density
  • Spectral representation
  • Joint intensities

Fingerprint Dive into the research topics of 'Determinantal point process models on the sphere'. Together they form a unique fingerprint.

  • Cite this