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On toral eigenfunctions and the random wave model

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Abstract

The purpose of this Note is to provide a deterministic implementation of the random wave model for the number of nodal domains in the context of the two-dimensional torus. The approach is based on recent work due to Nazarov and Sodin and arithmetical properties of lattice points on circles.

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ, 08540, USA

    Jean Bourgain

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  1. Jean Bourgain
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Correspondence to Jean Bourgain.

Additional information

This work was partially supported by NSF grants DMS-0808042 and DMS-0835373

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Bourgain, J. On toral eigenfunctions and the random wave model. Isr. J. Math. 201, 611–630 (2014). https://doi.org/10.1007/s11856-014-1037-z

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  • DOI: https://doi.org/10.1007/s11856-014-1037-z

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