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Nodal intersections for random waves against a segment on the 3-dimensional torus

Research output: Contribution to journalArticle

Original languageEnglish
Number of pages37
Accepted/In press14 Feb 2017


King's Authors


We consider random Gaussian eigenfunctions of the Laplacian on the three-dimensional flat torus, and investigate the number of nodal intersections against a straight line segment. The expected intersection number, against any smooth curve, is universally proportional to the length of the reference curve, times the wavenumber, independent of the geometry. We found an upper bound for the nodal intersections variance, depending on the arithmetic properties of the straight line. The considerations made establish a close relation between this problem and the theory of lattice points on spheres.

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