Hyperuniform point sets on the sphere: probabilistic aspects


The concept of hyperuniformity has been introduced by Torquato and Stillinger in 2003 as a notion to detect structural behaviour intermediate between crystalline order and amorphous disorder. The present paper studies a generalisation of this concept to the unit sphere. It is shown that several well studied determinantal point processes are hyperuniform.

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This material is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 while the first three authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Spring 2018 semester. The authors are very grateful to two anonymous referees for their valuable remarks and suggestions.

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Correspondence to Peter J. Grabner.

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Johann S. Brauchart was supported by the Lise Meitner scholarship M 2030 of the Austrian Science Foundation FWF.

Peter J. Grabner and Wöden Kusner were supported by the Austrian Science Fund FWF Project F5503 (part of the Special Research Program (SFB) “Quasi-Monte Carlo Methods: Theory and Applications”).

Communicated by Karlheinz Gröchenig.

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Brauchart, J.S., Grabner, P.J., Kusner, W. et al. Hyperuniform point sets on the sphere: probabilistic aspects. Monatsh Math (2020). https://doi.org/10.1007/s00605-020-01439-y

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  • Hyperuniformity
  • Determinantal point processes
  • Jittered sampling

Mathematics Subject Classification

  • 60G55
  • 11K38
  • 65C05
  • 82D30