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.
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We thank Joaquim Ortega-Cerdá and an anonymous referee for helpful comments.
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Communicated by Doug Hardin.
This research has been partially supported by Ministerio de Economía y Competitividad, Gobierno de España, through Grants MTM2017-83816-P, MTM2014-57590-P, and MTM2015-68805-REDT, and by the Banco de Santander and Universidad de Cantabria Grant 21.SI01.64658.
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Beltrán, C., Etayo, U. The Projective Ensemble and Distribution of Points in Odd-Dimensional Spheres. Constr Approx 48, 163–182 (2018). https://doi.org/10.1007/s00365-018-9426-6
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DOI: https://doi.org/10.1007/s00365-018-9426-6