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

Abstract:
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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.jfa.2017.02.011

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Elsevier
Journal:
Journal of Functional Analysis More from this journal
Volume:
272
Issue:
12
Pages:
5218-5254
Publication date:
2017-02-01
Acceptance date:
2017-02-14
DOI:
ISSN:
0022-1236
Keywords:
Pubs id:
pubs:733155
UUID:
uuid:c9ce3b08-3f0c-4625-93a7-9ff0e3570138
Local pid:
pubs:733155
Source identifiers:
733155
Deposit date:
2017-11-02

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