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Hyperuniform point sets on the sphere: probabilistic aspects

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Abstract

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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Acknowledgements

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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Authors and Affiliations

  1. Institute of Analysis and Number Theory, Graz University of Technology, Kopernikusgasse 24., 8010, Graz, Austria

    Johann S. Brauchart & Peter J. Grabner

  2. Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN, 37240, USA

    Wöden Kusner

  3. Fachbereich Mathematik, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Jonas Ziefle

Authors
  1. Johann S. Brauchart
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  2. Peter J. Grabner
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  3. Wöden Kusner
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  4. Jonas Ziefle
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Corresponding author

Correspondence to Peter J. Grabner.

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Communicated by Karlheinz Gröchenig.

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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”).

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Brauchart, J.S., Grabner, P.J., Kusner, W. et al. Hyperuniform point sets on the sphere: probabilistic aspects. Monatsh Math 192, 763–781 (2020). https://doi.org/10.1007/s00605-020-01439-y

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  • DOI: https://doi.org/10.1007/s00605-020-01439-y

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