The Projective Ensemble and Distribution of Points in Odd-Dimensional Spheres

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Abstract

We consider a determinantal point process on the complex projective space that reduces to the so-called spherical ensemble for complex dimension 1 under identification of the 2-sphere with the Riemann sphere. Through this determinantal point process, we propose a new point processs in odd-dimensional spheres that produces fairly well-distributed points, in the sense that the expected value of the Riesz 2-energy for these collections of points is smaller than all previously known bounds.

Keywords

Determinantal point processes Minimal Riesz energy Minimal Green energy 

Mathematics Subject Classification

Primary 31C12 Secondary 31C20 52A40 

Notes

Acknowledgements

We thank Joaquim Ortega-Cerdá and an anonymous referee for helpful comments.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

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