Nodal intersections for random waves against a segment on the 3-dimensional torus
Journal of Functional Analysis, ISSN: 0022-1236, Vol: 272, Issue: 12, Page: 5218-5254
2017
- 8Citations
- 2Captures
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Article Description
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.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S002212361730071X; http://dx.doi.org/10.1016/j.jfa.2017.02.011; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85014515883&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S002212361730071X; https://api.elsevier.com/content/article/PII:S002212361730071X?httpAccept=text/plain; https://api.elsevier.com/content/article/PII:S002212361730071X?httpAccept=text/xml; https://dx.doi.org/10.1016/j.jfa.2017.02.011
Elsevier BV
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