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arXiv · 1303.2881

On toral eigenfunctions and the random wave model

Jean Bourgain
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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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Jean Bourgain. 2013-03-12. On toral eigenfunctions and the random wave model. https://arxiv.org/abs/1303.2881

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